I do worse in the summer time. I live in MA and find that the hot humid summers are much more difficult...b/c on top of the heat, my allergies are TERRIBLE. This winter has not been that bad, I have been sick a few more times than normal, but not really bad.
I would think VA or the Carolinas would be good, I have always liked those areas. They are pretty and the weather seems to be more consistent than other areas of the country. AZ would be a definite no-no for me, because of the heat.