I lived in DC for over 10 years and in college worked as a hotel concierge at the Crowne Plaza on 14 st, NW.
There is only one hotel in DC (proper) with an indoor pool. That hotel is: loews l'enfant plaza. It is walking distance to the museums and in a decent neighborhood and is a very nice hotel. However, there will basically be no restaurants open in the immediate area after about 5 or 6 and not on the weekends except the McDonald's as it is surrounded by office buildings.
Bethesda, MD and Arlington, VA have some great hotel options with pools, just make sure that they are near the metro. They are rather spread out towns with just a few stops.
If you go to expedia.ca and put in that you want a pool you should get a list of hotels. in the area. If I have time later I will look too and post what I find that looks good transportation-wise.