I agree with the last post - you'd need to narrow that interest - e.g., are you interested in a certain disorder/symptom? A specific population? Treatment or etiology?
From my experience, there wasn't a lot of schools asking where else you applied. I don't think it'd be a red flag, provided you were able to demonstrate interest in something specific and there were researchers at the programs studying it.
As I'm sure you know, restricting yourself to a certain geographic location could make it significantly harder to get in somewhere. But it's a personal preference for some people, I guess.