What is the noun phrase whose head is China in the sentence "It looks a lot like the China May and I used to see in movies brought to Shanghai from Hollywood."
What you may be finding confusing regarding this sentence is the dropped 'that'. It is relatively common in English for words to be dropped if their presence can be inferred by the context. For clarity, I include it in italics with the noun phrase bolded (exactly as per snailboat's comment)
It looks a lot like the China that May and I used to see in movies brought to Shanghai from Hollywood.
What follows from where the 'that' should be is a relative clause, but it is still considered to be an element of the noun phrase (refer to the links for more information on this).
The sentence is potentially confusing for several reasons. But to break it out:
The subject is "it".
The verb is "looks ... like".
That is, "it", the thing that he is talking about, looks like something else.
The object of the verb is "the China". The thing that it looks like is China. But not just China in general, rather, the China that "May and I used to see in movies". Presumably "May" is a person's name, likely the writer's wife or girlfriend. Perhaps the larger context makes clear who she is.
And finally, what "movies" is he talking about? Movies "brought to Shanghai from Hollywood".
I stumbled over the sentence on first reading because it's fairly complex, and seeing the capitalized words "China" and "May" together made me for a moment think that "China May" was the name of something. I had to read it a second time to realize they were two separate names.