If you're less adventurous, backpacking around Europe is a fairly standard longer trip, plus in October you can hit Oktoberfest in Munich, which I've heard can be worth it. Unfortunately, I haven't had a chance to go myself when I've been in Germany though. Most of the major touristy areas (for Americans, at least) tend to be Western Europe (Dublin, London, Paris, Munich, Vienna, Venice/Rome). While that's definitely for good reason, try to go off the beaten path and not just hit the well known landmarks, you'll often find better food and more interesting people.
Asia is definitely on my personal list, it's definitely doable for dirt cheap, and it'll be a hell of an experience. The culture shock may be greater than Europe, but I'd say it's worth it.
Whichever way you go (or one like Cent./South America or Africa), there are a lot of dedicated travel forums where people can likely help with anything you might need. You can start with http://www.lonelyplanet.com/
Some words of advice from travelling a fair amount:
1) pack light, your back and legs will thank you
2) eat what the local people are eating
3) don't be afraid to try new things and meet new people
4) if you think you're going to go a country, check on the visa requirements so you don't end up with the headache of dealing with that while you're there
5) plan ahead enough that your trip runs relatively smoothly, but not that you're locked into an itinerary or on any sort of strict schedule
If you want to ask me about anything, I'm in the middle of planning/saving for a round-the-world type trip and I'll try to point you in the right direction.