It's a good question, but also difficult to answer satisfactorily and still open for debate in academia.

There is a narrative, partly reflected in your question, that Christian thinkers adopted neo-platonism and refashioned Christianity on that basis, as part of the 'Hellenisation' of the church. This view is normally cast in a negative light, as a corruption of 'pure' Christianity which is typified by 'Hebraic' thought.

That Hellenisation/Corruption paradigm goes back to von Harnack, and is largely discredited in the field of 4th century theology. Instead, the work being done at present is much more interested in analysing and articulating how Christian theologians adopted and adapted specific elements of Neoplatonic thought.

There's no doubt that they did so. 4th century thinkers tended to be drawn from the upper-echelons of Graeco-Roman society and had completed advanced education in rhetoric and philosophy. Neo-platonism was one of the dominant and influential philosophical streams of the time, and authors like Gregory of Nyssa, Gregory of Nazianzus, and Augustine, all demonstrate familiarity with aspects of Neo-platonism.

One of the areas where neoplatonism shows its influence is in the quite technical discussions about nature/essence and God as 'One'. What it means for God to be a simple being, how immutability works, etc., are all ideas developed in Christianity in conversation with neoplatonism, and by adapting neoplatonic categories and terminology.

Other specific elements of comparison include the Cappadocian identification of "power" with "essence", which allowed them to align the Son as the 'Power of God' with God himself. The notion of evil as an absence of good appears to inform Augustine's theology of evil, though that notion of evil is not universal across the neoplatonists.

But then, on the other hand, Christianity strongly rejected the idea of emanations and a gradated world of ontology. The Nicene solution (and by Nicene I do not mean simply 325, but those authors considered 'pro-Nicene', that is post-325 authors ultimately seen as in favour of Nicaea, and later Constantinople 381, as representing orthodoxy) firmly rejected that conception of reality and formulated a clear Creator/creation distinction (in which creation was created ex nihilo, and the divine Son was on the Creator-side of the division, thus rejecting Arianism and its successor beliefs).

The influence of Neoplatonism mainly had to do with the fairly rarified debates about the nature of God and the relationship of Father and Son in the mid to late 4th century. It was the 'air' in which Greek philosophy, and so theology, operated, and it provided a ready tool for Christian theologians seeking to articulate a precise and nuanced set of doctrines. The idea that Nicene Christianity was a radical reformulation of a 'pure' Christianity into a 'hellenised pseudo-Christianity' is for the most part wrong.

As /u/talondearg pointed out, this is a complex question and requires one to check biases in a multitude of ways. I am not sympathetic to the sorts of declension narratives put forward by 19th century Germans (like von Harnack, Baur, etc).

Since an answer has already been given, I'd like to put forward the idea that Nicene Christianity is actually a rejection of Middle or Neoplatonism. While Rowan Williams in his Arius: Heresy and Tradition overstates the case with respect to Arius' reliance on neoplatonism (Christopher Stead has critiqued Williams on this and Williams has since admitted he overstated the case) - Arius did indeed have Neoplatonic concerns, especially when it came to the inaccessibility of the First Principle, whom Arius believed to be the Father. This meant that for Arius, the Son was certainly divine in a sense, but He could not be God in the same way the Father is and also have come down here and done the sorts of things the Gospels record Him doing. In other words, while Arius was certainly a Christian and cared about Scripture, his version of the story seems to be driven largely by Neoplatonic concerns about the impassibility of the first principle and the Gospel was read into that. Nicaea seems to be affirming the radical idea that God qua first principle took on flesh. You see Christians then working out the 'how' of this radical story after Nicaea in figures like Apollinaris, Nestorius, Cyril of Alexandria, etc.

A good work on the metaphysics surrounding Nicaea is Khaled Anatolios' Retrieving Nicaea: The Development and Meaning of Trinitarian Doctrine.