Wow didn't know there were so many folks from DC on this board. I'll echo what has been said before. The DC subway system is great and for the most part very safe. Hotels however will be expensive. I'd suggest one of the discount sites such as Expedia etc. As for safety stay out of SouthEast. There is a new complex on the Anocostia River that is very nice but that area after dark is dicey outside of the complex. But you can spend a week visiting the monuments and museums alone.
Write via PM if you want specific info, be glad to help