What is the correct preposition to use in this sentence: for, of or about, and why?
I feel nostalgic __ my childhood.
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The normal usage would probably be "for", indicating that you are nostalgic and wistful, wanting to be back there in your childhood.
"about" is also perfectly OK, but this has less sense of actually wanting to return there.
So it would make sense to write "I am nostalgic for my childhood - I wish I could be a child once more!" and "I am nostalgic about my childhood, but life has moved on, and what is past is past, with some wonderful memories".
The normal usage would be nostalgia for, as nostalgia is a noun and nostalgic is an adjectival form of nostalgia or a noun meaning "a person who displays nostalgia for something" – an irrelevant sense in your example.
Data from ngrams indicates that popularity of forms nostalgia for,nostalgic for,nostalgic about,nostalgia about declines in that order, with nostalgia for occurring about five times more frequently than the other three forms together.
Reviewing uses of nostalgic about in google books, one sees that it frequently is used in the phrase be nostalgic about, that is, in cases where the adjective form nostalgic applies.