When a friend of mine moved to New York City, he started reaching out to top-notch designers (there are quite a few there) basically saying "Hey, I'm new to the town, here's what I do, here's what I've done, would you be interested in getting together to talk?" and surprisingly, a few of these people made time in their life to meet him. He has since fostered a relationship with industry leaders and now meets and works closely on side projects with some of the biggest names in design. I'm not saying this will always happen but I think you would be surprised at what people are willing to do if you show motivation. I agree with previous comments that you should be doing interesting things but also be prepared to just share your hopes and goals.

To answer your questions: 1) anywhere 2) yes. yes. 3) I think a good mentor will realize the nature of the relationship. I don't think they're always looking to gain something. 4) no idea.