Nero was a fan of Greek Athletics. He tried to set up the Neronia, a Roman counterpart of the Olympics and other Pan-Hellenic festivals of the Greek world, in 60 AD. These games only held twice as they did not continue after his death. Domitian would try again with the Capitolia or Agon Capitolinus in 86 AD held in the Stadium of Domitian, a gift to the city.
The Romans were already a bit skeptical of Greek sports during Nero's time: too much nakedness, too much oil, too many massages, something you could use slaves for, but certainly not something an emperor should participate in. Lucan wrote during the time of Nero, writing the words of Julius Caesar:
"Nor will your reach for the world demand much blood. You’ll meet a force recruited in the colleges of Greece, enfeebled by their classes in the wrestling school and panting under the weight of their swords, or a motley clutter of barbarians who’ll run from the sound of their trumpets and hullaballoo of their own advance. "
-Lucan, Pharsalia 269-274 Real men fought - the Greeks sapped all their strength with "training". Ironically, Lucan won a poetry award in the Neronia, and became a friend of Nero's before a rift that ultimately resulted in Lucan being forced to commit suicide at 25 years old for participating in a conspiracy against Nero.
Nero's interests didn't do go over well, at least with the senatorial class:
"Because he was thought to equal Apollo in music, and the sun in chariot-driving, he resolved also to imitate the achievements of Hercules. And they say that a lion was got ready for him to kill, either with a club, or with a close hug, in view of the people in the amphitheatre; which he was to perform naked."
-Suetonius Nero 53 More disdain expressed by Cassius Dio:
"Such was Nero's general character. I shall now proceed to details. He had such enthusiasm for the horse-races that he actually decorated the famous race-horses that had passed their prime with the regular street costume for men and honoured them with gifts of money for their feed."
-Cassius Dio, Roman History, LXI.6.1 In AD 67, Nero went on a grand tour of Greece and further chafing the norms of decorum with his participation in games, and his theatrical (fraudulent?) garnering of awards:
"But he crossed over into Greece, not at all as Flamininus or Mummius or as Agrippa and Augustus, his ancestors, had done, but for the purpose of driving chariots, playing the lyre,making proclamations, and acting in tragedies. Rome, it seems, was not enough for him, , nor Pompey's theatre, nor the great Circus, but he desired also a foreign campaign, in order to become, as he said, victor in the Grand Tour
-Cassius Dio, Roman History, LXIII.8.2-3 "Nero stayed in Greece for more than a year participating in all the major and minor festivals. He took part in the Actian games at Nicopolis which had been established by Augustus to celebrate his victory at Actium over Mark Anthony. In addition, he entered himself as competitor in many events and won the title "Periodonikes" victor [circuit-victor], in all four major Games [Olympia, Delphi, Nemea and the Isthmus]. He loved and practiced wrestling all the time and everywhere in Greece he watched the athletic competitions like the officials of the games. He not only won at competitions in which he took part, but even in those in which he did not. The name of Olympian victor rang as gloriously in his ear as any title of Roman imperial distinction. He gained about 1,800 prizes in various festivals."
-Mouratidis, Nero: The Artist, the Athlete and His Downfall , p.18The Penn Museum lists his victories this way:
"Nero's victories in Greece - heralds, tragedy, lyre, tethrippon (a four horse chariot race) , Foals tethrippon (a four horse chariot race with foals) , 10 horse chariot (all invalidated later)"
-Penn Museum, The Real Story of the Olympic Games 
This coin commemorates the Nemean Games of August 66 or 67 AD, the athletic and musical competition held every 4 years in the grove of Zeus Nemeios in the city of Argos.
Nero is said to have competed in these games. The winners of the Nemean games were crowned with celery leaves as Zeus is crowned on this coin. Laurel leaves were used at other games. There were four major games : Olympic, Pythian, Isthmian and Nemean games
Egypt, Alexandria, Nero, AD 54-68, BI tetradrachm, dated year 14=A.D. 67/8, scarce type
Obv: NEPΩ KΛAV KAIΣ ΣEB ΓEP AV, L IΔ (date), radiate head left, wearing aegis
Rev: NEMEIOΣ ZEVΣ, head of Zeus Nemeios right, crowned with celery leaves
Ref: Milne 279; Emmett 136; RPC 5308
This coin commemorates the Isthmian Games in the Spring 66 or 67 AD, held at Korinthos (Isthmus of Corinth) in honor of Poseidon.
Egypt, Alexandria, Nero, AD 54-68, BI Tetradrachm, RY 14 = 67/8
Obv; ΝΕΡΩ ΚΛΑY ΚΑΙΣ ΣΕB ΓΕΡ AY / L IΔ, radiate bust of Nero to left, wearing aegis
Rev: ΠΟΣΕΙΔΩΝ ΙΣΘΜΙΟΣ Bust of Poseidon Isthmios to right, wearing taenia, with slight drapery on his left shoulder and with trident over his shoulder
Ref: Dattari (Savio) 243. Emmett 129.14
This coin commemorates the Pythian Games held every 4 years at Delphi in 67 or 68 AD, in honor of Apollo.
Egypt, Alexandria, Nero (54-68), BI Tetradrachm, dated RY 14 (67/8)
Obv: ΝΕΡΩ ΚΛΑV ΚΑΙΣ ΣΕΒ ΓΕΡ ΑV / LΙΔ, radiate bust right with aegis.
Rev: ΠΥΘΕΙΟΣ ΑΠΟΛΛΩΝ, laureate bust of Pythian Apollo with quiver right.
Ref: RPC 5312
This coin commemorates the Olympic Games held every 4 years at Olympia in 67 or 68 AD in honor of Zeus.
Egypt, Alexandria, Nero (54-68), BI Tetradrachm, dated RY 14 (67/8)
Obv: ΝΕΡΩ ΚΛΑV ΚΑΙΣ ΣΕΒ ΓΕΡ ΑV / L ΙΔ(date) below chin, radiate bust left with aegis.
Rev: ΔΙΟΣ ΟΛVΜΠΙΟV, laureate bust of Zeus Olympios right with slight drapery.
Ref: Dattari (Savio) 256, RPC I 5307
During his tour, Nero granted freedom to all of Greece, declaring "other rulers have freed cities, but only Nero a province":
"An unexpected gift (dorea), Hellenes, – though indeed there is nothing which cannot be hoped for from my munificence (megalophrosyne) – I grant to you, so great that you would not have dared to ask for it. All you Hellenes who inhabit Achaea and what has up to now been called the Peloponnese, receive freedom (eleutheria) and exemption from tribute (aneisphoria)"
-Mratschek, Nero the Imperial Misfit: Philhellenism in a Rich Man’s World (Buckley, E & Dinter, MT (eds) 2013, Ch. 3)As winner of the grand-slam of Greek athletics, Nero re-entered Rome in a chariot of white horses, surrounded by victory wreaths, the same chariot used by Augustus for his triumph. This surely added to the Roman elites' disdain for Nero and Greek athletics, even if there might have been some popular enjoyment of the spectacle.
References
Image of Apollo playing a lyre, copy of the Greek original, 3rd-2nd century BC. Roman Civilisation. Roma, Museo Nazionale Romano Palazzo Massimo Alle Terme, license purchased from Shutterstock
Mouratidis, John. “Nero: The Artist, the Athlete and His Downfall.” Journal of Sport History, vol. 12, no. 1, 1985, pp. 5–20.
Remijsen, S. (2015). The End of Greek Athletics in Late Antiquity (Greek Culture in the Roman World). Cambridge: Cambridge University Press.
Milavic, A. (2012) ."The Olympic Games: The First 1,166 Years". The Celator, Vol 26, No. 5, p. 6-25
Kennell, N. (1988). Neron Periodonikes. The American Journal of Philology, 109(2), 239-251.
Buckley, E & Dinter, MT (eds) 2013, A companion to the Neronian age. Blackwell companions to the ancient world, WILEY-BLACKWELL, Chichester. Chapter 3
Gallivan, Paul A. “Nero's Liberation of Greece” Hermes, vol. 101, no. 2, 1973, pp. 230–234.
Sources for the History of Greek Athletics, Rachel Sargent Robinson, Ares Publishers, Chicago, 1955, pp. 164-167
Sports in the Greek and Roman Worlds, Volume 2, Thomas Scanlon, Oxford University Press, 2014, pp. 165-179
The Real Story of the Olympic Games, Penn Museum
Excavations at Nemea (note: games were not held at Argos during Nero's time)
KU Leuven, Ancient Olympics
Arete: Greek Sports from Ancient Sources, Stephen Miller, pp. 162-164
Smithsonian Magazine, New Nicer Nero