That's awesome! Travel is such an important thing when you're young and creating your worldview. I'm stoked for you.
I'm from the USA, and traveling in North America is harder than what you're used to in Europe. We don't have a good transportation system and finding inexpensive accommodations is hard. There a few hostels, but they are really far apart and only in a few major cities like San Francisco, New York, and Los Angeles. The US is really interesting and has tons of natural beauty, but it will cost you a lot to rent a car and stay in hotels.
South East Asia is a booming area for young adult travel. Thailand seems to be a favorite of world travelers because it's inexpensive, there's tons of historical sites, the beaches are great, and the people are really friendly. A lot of Americans are moving over their to enjoy the climate and social atmosphere.
I don't know how much of Europe you have seen, but Easter europe seems a little less touristy (that's quickly changing) and seems to be cheaper. I really want to see Croatia and Slovenia because the beach and mountains look amazing. There's still a lot of ex-soviet landmarks that haven't made it onto the tourist maps. They are quickly showing up on the tourist radar and I'm afraid that the window for authentic travel experiences is ending. Greece also looks really fun. I would love to Greek island hop for a few weeks.
Columbia, Brazil, and Chile are turning into backpacker hotspots. They all seem really cheap, have tons of stuff to do, cater to people our age, and have really interesting cultures.
Two places I also want to go are New Zealand and Australia. Aussies, especially, seem like the most joyful and kind people I have ever met. I just love their attitudes towards life. I met a lot of them in European hostels and they seem like a fun bunch. New Zealand's got some wonderful mountain ranges that look breathtaking.
Whatever you decide, I hope you go somewhere fun and that it's an enlightening experience for you. Cheers!