StingingVelvet: Yeah, that's a main concern of mine. I don't want to be seen as the evil and corrupt American fatty by everyone.
I don't think you need to be worried, unless of course people spat on the ground every time they go to the airport (George W. Bush avenue). Plus the country is trying to push for the EU and NATO membership for ages. The only time I'd be worried about visiting Georgia would be as a Russian tourist.
I think it would be an interesting adventure to teach in Georgia. I don't know the specifics, but unless a full blown war breaks out there, you should be fine (and even then, they usually allow the evacuation of foreigners, especially US and EU). But as already mentioned, you should really study their culture and customs.