I spent time in Eastern Europe while in college. You'll meet plenty of people on your way and everything is cheap compared to the US. You can find $10 hostels, tons of people on couch surfing and drink $1 liter-of-beers, meet the locals or hit the larger cities for guaranteed English speaking travelers that are usually more than willing to share travel experiences. I went to Romania, Check Republic and Hungary. I was with 3 other people and we bought a used car for next to nothing and drove everywhere.
I live in Japan now and go to SE Asia often. I wouldn't not recommend it, but it would be really intense for first time alone travel.
I'd go spring break if you do Europe.