Those are like... biiiiiiiiiiig questions that I could go on about for ages. But the short answers are
1) A lot of people do come over from the US- when I studied in Kobe the group was mostly Americans.
2) There's a lot of good schools, you basically need to decide on where you'd want to live first. I chose Kansai; I know a lot of people who went to Hokkaido or around Tokyo.
3) I think Osaka/Kobe is the best place to stay because that's two big cities close to each other, plus Nara, Kyoto & Nagoya aren't too far away. Tokyo's a long trip, but you can get there in a day and back if you really rush things. It's not exactly in the middle, but it's a great location to stay for trips, at least if you're mostly limiting yourself to Honshuu.