"I don't go to noisy places."
Is 場所 interchangeble in this situation? E.g., could I say 「うらさい場所に行けません」?
First of all, 行けません means "not able to go" whereas the original question uses 行きません, implying you choose not to go even if you could ;)
To answer your question, I don't think you can without changing the nuance of the sentence, but I'm not sure. I'm not a native Japanese speaker, but using 場所 somehow feels more specific and wouldn't seem as natural in this sentence. That is, うるさいところ means noisy places in general, but うるさい場所 means specific locations/venues that are noisy. (E.g. そんなにうるさい場所で仕事できますか。 / Can you work in somewhere as noisy as that?) Again, I could be completely wrong, but that's what I think the difference is.
Turns out i can't copy text from the comments.
The kanji 場所 is pronounced "basho", so hopefully that will help others looking it up.