I would highly recommend Europe as well. I had never been until this year and I'm kicking myself for not going a lot sooner (I'm in my 30's). The culture over there is pretty different, and it's great to see the history over there. Price wise, Europe can be expensive, or it can be cheap. Hostels would be the way to go - and you can check out sites like
www.hostelworld.com to get an idea of cost. A Eurail pass would also be highly recommended and they have good deals for students. You mentioned that you wouldn't be into backpacking - and believe me I didn't think I would be either (it was my wife that convinced me it would be ok!), but it was really a lot of fun and you get to meet some great people. You'd be surprised how many people you meet going to do your laundry! I just think that Europe is a great experience for everyone, especially students. It will give you a bit of a different perspective on things when you get back.
Good luck in choosing your upcoming adventure! Hope you have a great time.