You cite weather as most important if I read your list right. I enjoy living here in many ways, but I really find the winter way too harsh for me. (I am a Virginia native). It gets so gray and cold here and yet we barely get snow. If you are coming from Michigan or New England, I know this will be a much milder winter. But if 38 degrees and gray bothers you from Christmas through Easter, you may want to go a bit further south.
The culture and outdoor activities here are great. I'd check the Lonely Planet DC guide for the best spots to hit up on your visit. Also look at the Washington City Paper.