I was having some doubts about the usage of のに with verb of motion. The book I'm using, "a dictionary of basic japanese grammar", says that in case of verb of motion the のに form contrasts with the form verb in 連用形 plus a verb of motion. Thus, the book states that both these two sentences are fine, but the second one implies that the speaker made a lot out of the entire process or that it was not worth it.
However, to me the second sentence does not make much sense and it seems rather unnatural. I would have made it: 映画を見るには銀座へ行った。