Wow. Great thought. I lived abroad for ten years, and just finished a seven month stint in Budapest. I take it that you are single and your experience is with coding. Here is the scoop:
1) Go somewhere where there are fewer other Americans. Avoid England, France, Spain and Germany. You'll have more fun being the odd American in town.
2) The places where you will be most warmly received are the former Communist countries of Central Europe: Czech Republic, Slovakia, Poland, Hungary, etc. It was the Americans that saved them from the Russians 20 years ago, not the Europeans, and they remember that.
3) There are jobs aplenty available in these countries. For an English-speaking American programmer, these are usually jobs managing local talent. You will NOT find these jobs in the US - you need to go there and look for them. Employers want to see that you are already in the country and happy being there, rather than hiring you in the US, expensively shipping you to another country and potentially having you quit soon thereafter. Oh, and these jobs pay quite well, particularly compared to local costs of living.
4) In reference to #1, and this is hard to make yourself do, but strongly recommended - try to find a position that places you in a smaller town, not the capital. It's better to be the odd American in Brno than one of thousand in Prague; you'll have an easier time making friends and it will force you to learn the language, since there will be fewer English speakers around. My first six months in the Czech Republic and my first six months in Taiwan were both in small towns, and they remain my favorite countries that I have lived in (I've lived in eight now).
5) Finally, I just returned from Budapest this week. I believe that Crytek has positions available in their Budapest office. My Hungarian tutor was teaching their staff a couple of times a week (and they were doing a terrible job of learning Hungarian).