staying at colleges in U.S.
Nina,
I'm a student at Penn State University (in State College, Pennsylvania), and as a H.S. senior did a short road trip/college tour as a 17-year old. Before you go on your trip, I'd suggest getting in touch with the colleges you plan to visit. I don't know about most of them, but some of them have a program where you can stay in the dorms with a student when you visit. If you contact the colleges ahead of time and really want to learn about them, you could also get signed up for tour and information session, where they sometimes give you a free meal in the cafeteria after the tour. Those are some great ways to save money and really get a feel for the college, if that's your goal.
Hostels are a great place to stay if you don't mind sharing a bathroom, but I don't know if there are any age restrictions. I've stayed in hostels in Cali and here in PA, and they are really in great locations, usually in cities. They're a great way to save money and meet people close to your age. Check out www.hiayh.org. If you're going over the summer, it's probably worth making reservations, but only if you know exactly when you'll be certain places.
That's my advice, let me know if you have any questions or whatever. Also, I know plenty of students at different colleges that you might be able to stay with, so feel free to get in touch if you want to. Good luck!
Ben