I spent almost 2 months in 2003 tromping around Thailand, Cambodia and Vietnam and it was awesome. Even better, total cost, including airfare (got a sweet deal for $700) was just over three grand.
I strongly encourage you consider SE Asia. You get: serious culture shock, incredible history (esp in Cambodia and the Nam), and almost the most important part, unbelievably cheap prices. You can get your own room with bathroom for usually a couple dollars a day, and if you want to go lux, for $10-$15 a day. Plus a full meal will rarely cost more than a dollar or two, including drinks.
Cambodia is especially awesome because of Angkor Wat/Siem Reap. On my trip, I planned on spending three days in Siem Reap and ended up staying for 2 weeks.
Another bonus is that, unlike Europe, the locals think Americans walk on water, and you will always make friends wherever you are.
Yet another bonus is you can travel on your own, or you can choose to hook up with other fellow travelers. I spent a week traveling around with this british guy, who I'm still in touch with, and then after a couple weeks on my own, had a great 'travel affair' with an Irish woman for about a week until we got sick of each other. What was funny was that after we "broke up", we kept running into each other every couple hundred miles for the next couple weeks because we were heading in the same direction.