Based on time constraints, and the fact that you'd be glad to go
somewhere in (presumably East) Asia, I'd throw Japan out there. Since you mention history/culture, you might want to fly into Osaka Kansai (KIX), which makes getting to Kyoto (arguably the historical/cultural epicenter in the country), Nara and indeed, Osaka much easier than a flight into Tokyo.
Which isn't to say you should ignore Tokyo, but then to maximize time you'd have to take a bullet train to the Kansai area (where Kyoto, Nara and Osaka are located), or one of many daily flights (including low-cost carriers) to Osaka. If this is more your speed, here is a list of budget (but not necessarily guesthouse) accommodations in Tokyo:
http://www.flyertalk.com/forum/budge...els-tokyo.html.
I don't drink, but Tokyo and Osaka (and likely Kyoto too) have thriving bar scenes. As for encountering Europeans/fellow Westerners in them, that depends on the neighborhood.
As for SkyTeam flights to KIX from the US, non-stops include China Airlines from JFK or Delta from SEA.