It should be some precision about the “Gardens of Academos” which gave name to the famous school founded by Plato. First, Academy is not a building, as one may think, but an area or neighborhood of Athens, outside the walls, approximately 1.5 kilometers, which is called the Academy, Ἀκαδημία, or Hekademeia (Ἑκαδήμεια), from the name of the local hero Academos or Hekademos, as Diogenes Laertius said in “Life of eminent Philosophers”, 3.7 ff.:
The Academy was in the outskirts of Athens, 1.5 kms. north; it was reached by the door Dypilom a path in which there were numerous tombs of illustrious men, as Pausanias tells us in his famous Guide the Greek world, Description of Greece in 1, 29, 2-3:
 Outside the city, too, in the parishes and on the roads, the Athenians have sanctuaries of the gods, and graves of heroes and of men. The nearest is the Academy, once the property of a private individual, but in my time a gymnasium. As you go down to it you come to a precinct of Artemis, and wooden images of Ariste （Best） and Calliste （Fairest）. In my opinion, which is supported by the poems of Pamphos, these are surnames of Artemis. There is another account of them, which I know but shall omit. Then there is a small temple, into which every year on fixed days they carry the image of Dionysus Eleuthereus.
 Such are their sanctuaries here, and of the graves the first is that of Thrasybulus son of Lycus, in all respects the greatest of all famous Athenians, whether they lived before him or after him. The greater number of his achievements I shall pass by, but the following facts will suffice to bear out my assertion. He put down what is known as the tyranny of the Thirty, setting out from Thebes with a force amounting at first to sixty men; he also persuaded the Athenians, who were torn by factions, to be reconciled, and to abide by their compact. His is the first grave, and after it come those of Pericles, Chabrias and Phormio. (English Translation by W.H.S. Jones, Litt.D., and H.A. Ormerod, M.A., Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1918.)
The site was a place of very ancient cult, perhaps from the Bronze Age, as it is evidenced by its relationship with the demigods the Dioscuri, the forest of olive trees dedicated to Athena, and to other gods.
It was a space dedicated to various gods: Athena, who had an altar beside another of Hephaestus and Prometheus, Hermes, Hercules, the Muses and Eros.
Pausanias, Description of Greece, I, 30,2
 In the Academy is an altar to Prometheus, and from it they run to the city carrying burning torches. The contest is while running to keep the torch still alight; if the torch of the first runner goes out, he has no longer any claim to victory, but the second runner has. If his torch also goes out, then the third man is the victor. If all the torches go out, no one is left to be winner. There is an altar to the Muses, and another to Hermes, and one within to Athena, and they have built one to Heracles. There is also an olive tree, accounted to be the second that appeared. (English Translation by W.H.S. Jones, Litt.D., and H.A. Ormerod, M.A. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1918.)
The land belonged at the time to Hipparchus, son of Peisistratos, who surrounded it by a wall and made a gymnasium; it was embellished and enhanced by Cimon, who led water by diverting Cephissus, nearby river, and planted trees and created a stadium for racing, as Plutarch tells us, in Cimon 13.8
 He was the first to beautify the city with the so-called ‘liberal’ (for entertainment) and elegant resorts which were so excessively popular a little later, by planting the market-place with plane trees, and by converting the Academy from a waterless and arid spot into a well watered grove, which he provided with clear running-tracks and shady walks. (English Translation by. Bernadotte Perrin. Cambridge, MA. Harvard University Press. London. William Heinemann Ltd. 1914. 2.)
The Spartans, owners of Athens after the Peloponnesian War, respected Academy in memory of the assistance offered by Academos their heroes Castor and Polux, according to Plutarch, Theseus, 32.3
 But Academus, who had learned in some way or other of her concealment at Aphidnae, told them about it. For this reason he was honored during his life by the Tyndaridae, and often afterwards when the Lacedaemonians invaded Attica and laid waste all the country round about, they spared the Academy, for the sake of Academus. (English Translation by. Bernadotte Perrin. Cambridge, MA. Harvard University Press. London. William Heinemann Ltd. 1914. 1.)
Plato certainly looking shady walks of Academy, bought some land to "philosophize" there with his disciples and friends. (Plutarch. From exsilio 10)
The Academy near Athens, that was purchased for three thousand drachmas, was the place where Plato, Xenocrates, and Polemo dwelt; there they held their schools, and there they lived all their lifetime, except one day every year, when Xenocrates came into the city at the time of the Bacchanals and the new tragedies, to grace the feast, as they say. Theocritus of Chios reproached Aristotle, who affected a court-life with Philip and Alexander, that he chose instead of the Academy rather to dwell at the mouth of Borborus. For there is a river by Pella, which the Macedonians call by that name (Borborus). (Translated from the Greek by several hands. Corrected and revised by. William W. Goodwin, PH. D. Boston. Little, Brown, and Company. Cambridge. Press Of John Wilson and son. 1874. 3.)
Plato built in the grounds of the Academy a small temple to the Muses, called Mouseion, in which Speusippus placed statues of the Graces. (Diogenes Laertius, IV 1,3,8 / and III, 5 and 20)
A Persian named Mithridates commissioned to sculptor Silanion to make a statue of Plato, he took it to the temple and dedicated it to the Muses. (Diogenes Laertius III, 20)
After the death of Plato, this statue was placed in the center of his school and the great philosopher was buried in the vicinity of the Academy, as tells us Pausanias, I, XXX, 3:
Not far from the Academy is the monument of Plato,
It is also given us a curious story about the prohibition of funerals in the city in a letter of Servius to Cicero on the occasion of the death of his colleague M. Marcellus who had received two wounds, while in Athens and how he was cremated at the Academy; it incidentally proves that it is not a building but a space, land or district of Athens:
CICERO, Letters to Friends – Epistulae ad Familiares, IV, 12,3:
SERVIUS SULPICIUS RUFUS TO CICERO (AT TUSCULUM) ATHENS, 31 MAY
Servius sends many good wishes to Cicero. Though I know that I shall be giving you no very pleasant news, ….
….honourable funeral. I could not induce the Athenians to grant him a place of burial within the city, as they alleged that they were prevented by religious scruples from doing so; and it is a fact that they had never granted that privilege to anyone. But they allowed us, which was the next best thing, to bury him in any gymnasium we chose. We chose a place in the most famous gymnasium in the world—that of the Academy—and there we burnt the body, and afterwards saw to these same Athenians giving out a contract for the construction of a marble monument over him. So I think I have done all for him alive and dead required by our colleagueship and close connexion. Goodbye. 31 May, Athens. (Translated by Evelyn Shirley Shuckburgh. London. George Bell and Sons. 1908-1909.)
ab Atheniensibus, locum sepulturae intra urbem ut darent, impetrare non potui, quod religione se impediri dicerent, neque tamen id antea cuiquam concesserant. quod proximum fuit, uti in quo vellemus gymnasio eum sepeliremus, nobis permiserunt. nos in nobilissimo orbi terrarum gymnasio Academiae locum delegimus ibique eum combussimus posteaque curavimus, ut eidem Athenienses in eodem loco monumentum ei marmoreum faciendum locarent. ita, quae nostra officia fuerunt pro collegio et pro propinquitate, et vivo et mortuo omnia ei praestitimus. vale. D. pr. K. Iun. Athenis.
The Academy received a mortal blow when in 86 BC the Roman general Sulla captured and destroyed Athens. The director of the Academy, Philo of Larissa, left Athens the following year and died leaving no successor, which resulted in the death of the institution. But Sulla did not respect either the Academy and the Lyceum. Plutarch tells us it, in Sulla, 12.1-3
12 1 As for Sulla, he at once received deputations and invitations from the other cities, but Athens was compelled by the tyrant Aristion to side with Mithridates. Against this city, therefore, Sulla led up all his forces, and investing the Piraeus, laid siege to it, bringing to bear upon it every sort of siege-engine, and making all sorts of assaults upon it. 2 And yet if he had been patient a little while, he might have captured the upper city without hazard, since it lacked the necessities of life and was already reduced by famine to the last extremity. But since he was eager to get back to Rome, and feared the spirit of revolution there, he ran many risks, fought many battles, and made great outlays that he might hasten on the war, in which, not to speak of his other munitions, the operation of the siege-engines p363called for ten thousand pairs of mules, which were employed daily for this service. 3 And when timber began to fail, owing to the destruction of many of the works, which broke down of their own weight, and to the burning of those which were continually smitten by the enemy's fire-bolts, he laid hands upon the sacred groves, and ravaged the Academy, which was the most wooded of the city's suburbs, as well as the Lyceum. (translation is that of the Loeb Classical Library edition (Cambridge, MA and London), by Bernadotte Perrin).
Appian also in his History of Rome XII, 5.30 (War of Mithridates):
Appian's History of Rome: The Mithridatic Wars, XII, 5,30
Sulla chopped down the grove of the Academy and constructed his largest engines there. He demolished the Long walls, and used the stones, timber, and earth for building mounds. (Translation by Horace White)
When Antiochus returned to Athens in 88 BC restored the teaching, but not in the Academy. Cicero presents Antiochus teaching at a gym that was called Ptolemy.
Cicero himself describes an emotional visit to the Academy one afternoon because it "is deserted at that hour."
Cicero, De Finibus, 5, 1
My dear Brutus, — Once I had been attending a lecture of Antiochus, as I was in the habit of doing, with Marcus Piso, in the building called the School of Ptolemy; and with us were my brother Quintus, Titus Pomponius, and Lucius Cicero, whom I loved as a brother but who was really my first cousin. We arranged to take our afternoon stroll in the Academy, chiefly because the place would be quiet and deserted at that hour of the day. Accordingly at the time appointed we met at our rendezvous, Piso's lodgings, and starting out beguiled with conversation on various subjects the •three-quarters of a mile from the Dipylon Gate. When we reached the walks of the Academy, which are so deservedly famous, we had them entirely to ourselves, as we had hoped. (English translation by H. Harris Rackham. Loeb Classical Library brother Aristus.1931)
1. Cum audissem1 Antiochum, Brute, ut solebam,2 cum M. Pisone in eo gymnasio, quod Ptolomaeum vocatur, [p. 156] unaque nobiscum Q. frater et T. Pomponius Luciusque Cicero, frater noster cognatione patruelis, amore germanus, constituimus inter nos ut ambulationem postmeridianam conficeremus in Academia, maxime quod is locus ab omni turba id temporis vacuus esset. itaque ad tempus ad Pisonem omnes. inde sermone vario sex illa a Dipylo stadia confecimus. cum autem venissemus in Academiae non sine causa nobilitata spatia, solitudo erat ea, quam volueramus.
The property of Plato with its school would be outside the walls of the Academy, somewhere between the currently visible gym and northeast hill called Hippios Kolonos. Unfortunately nothing remains of the Academy of Plato and there is not even agreement among archaeologists about your specific site, despite the efforts and despite what the current guidebooks of Athens say.
The name “Academy” was later given, in memory of Plato and his disciples, to other sites devoted to the study of literature and philosophy. Cicero called so a field he owned near Puteoli (Puzzole); Pliny, XXXI, 6 (3)
The country-seat where these last are found is worthy of some further mention: travelling from Lake Avernus towards Puteoli, it is to be seen on the sea-shore, renowned for its fine portico and its grove. Cicero gave it the name of Academia, after the place so called at Athens: it was here that he composed those treatises of his that were called after it; it was here, too, that he raised those monuments to himself; as though, indeed, he had not already done so throughout the length and breadth of the known world. (The Natural History. Pliny the Elder. John Bostock, M.D., F.R.S. H.T. Riley, Esq., B.A. London. Taylor and Francis, Red Lion Court, Fleet Street. 1855.)
dignum memoratu, villa est ab Averno lacu Puteolos tendentibus inposita litori, celebrata porticu ac nemore, quam vocabat M. Cicero Academian ab exemplo Athenarum, ibi compositis voluminibus eiusdem nominis, in qua et monumenta sibi instauraverat, ceu vero non et in toto terrarum orbe fecisset.
Also on Ad Atticum, I,4,3
… I am very glad to hear what you say about the Hermathena. It is an ornament appropriate to my "Academia" for two reasons: Hermes is a sign Common to all gymnasia, Minerva specially of this particular one. So I would have you, as you say, adorn the place with the other objects also, and the more the better. The statues which you sent me before I have not yet seen. They are in my villa at Formiae, whither I am at this moment thinking of going. I shall get them all transferred to my Tusculan villa. If I find myself with more than I want there I shall begin adorning Caieta. Please reserve your books, and don't despair of my being able to make them mine. If I succeed in that, I am superior to Crassus in wealth and look down on everybody's manors and pastures. (Translated by Evelyn Shirley Shuckburgh)
1.4.3 quod ad me de Hermathena scribis, per mihi gratum est. est ornamentum Academiae proprium meae, quod et Hermes commune omnium et Minerva singulare est insigne eius gymnasi. qua re velim, ut scribis, ceteris quoque rebus quam plurimis eum locum ornes. quae mihi antea signa misisti, ea nondum vidi; in Formiano sunt, quo ego nunc proficisci cogitabam. illa omnia in Tusculanum deportabo. Caietam, si quando abundare coepero, ornabo. libros tuos conserva et noli desperare eos