You should clarify your question a bit to include your own racial background. If you aren't white (and, preferably, blond), the answers will vary a bit more widely.
Asian countries, by and large, still hold a significant "attraction factor" that defies basic logic, though in some countries (most notably Japan), the instances of abuse by both civilians and military personnel, "players" dumping girls post-sex, and other stories of 'crazy American dudes' has enough of a history that Americans are not the hot commodity we once were…
Eastern Europe is another good choice – decent mix of indigenous peoples, muslims, and Christians – the Christians will tend to be the most interested, especially in white guys. Bonus points – due to long decades of largely Soviet rule, the desired qualities in a boyfriend/potential mate are wildly different from Western Europe and the US – physical qualities and attractiveness has a LOT more leeway, let's just leave it at that.
On the flip side, more "ethnic" Americans tend to still do better than averages would suggest in Northern Europe – the grass really is always greener, I guess.
Overall, though, it's a tough time to be a single American man overseas. You have a lot to answer for, the Bush years still linger, and people will seemingly endlessly pepper you with questions about US foreign policy – most of which you won't have a clue about, since so little of what we do "out there" ever reaches our ears back home. This does have some carry-over into dating – sure, the girls might like you, but if you get flustered over politics/religion/gay rights/etc when having dinner with her parents, yikes.
You could always stitch a maple leaf onto your backpack, practice saying "a boot" until you can merge it into a single word, and try to pass as Canadian – but you didn't get that advice from me.