Dear Mangosteen :bow:
May I ask, what do you mean by "Neo-Mysticism"?
Well, I do know that Neo-Platonism had a defining influence upon Christian Mysticism and Sufi Islam.
Plotinus' Enneads were read by St. Augustine of Hippo in the 4th century AD. He started out life as a convert to Manichaeism. He then left the religion of Mani after an existential crisis, to become a bit of a pleasure-seeking playboy. Then he became a Neo-Platonist. It was during this period that he had his first stirrings of mystical awareness as recorded in his autobiography, The Confessions of St. Augustine. His lifelong mystical experiences, even as a Christian, are coloured and informed by his Neo-Platonic philosophy.
In the fifth century AD an anonymous Syrian monk who took the pen-name of "Dionysius" wrote a series of mystical Christian treatises about apophatic prayer (imageless prayer that rests beyond the reach of thought in an unknowing union with God) that were heavily coloured by Neo-Platonic concepts and imagery. He was mistakenly thought by John Eriugena, an Irish philosopher of the 9th century, to be Dionysius the Areopagite from the Bible, a disciple of St. Paul. Eriugena translated these texts into Latin. As a result The Dionysian Corpus became a crucial foundation of medieval Orthodox and Catholic mysticism - spreading Neoplatonic philosophy widely in the Christian world.
Meister Eckhart and his followers Johannes Tauler and Blessed Henry Suso often referred back to the works of Plotinus as instances of genuine mystical genius. Eckhart called him a "great priest". They were very popular with medieval mystics and scholastics of the intellectual bent. Eckhart's theology was heavily Neo-Platonic in flavour, to the extent that his mystical theology has been viewed as an attempt to "syncretize" Christianity with what was compatible in Neo-Platonism.
Sufi Islam was likewise highly influenced by Neo-Platonism. Arab authors were deeply appreciative of Aristotle. Plotinus' Enneads were circulated throughout the Islamic world in the late first millennium and were attributed to Aristotle or anonymously to a "wise philosopher of the Greeks". As a result of this mistaken identity, as with the Christian West, Islamic spirituality came to be heavily influenced by Neo-Platonic philosophy. Ibn Arabi, the great 13th century Sufi mystic and philosopher from Spain, formulated what was essentially a "school" of Islamic Neo-Platonism with a very monistic (to an extent while still being theistic) view of reality.
As for Buddhism, I do not think that Neo-Platonism has influenced Buddhism at all. Buddhism was founded about eight hundred years before the first school of Neo-Platonism in the third century AD.