Being a native Washingtonian, I would not advise that you use any of the distant VA resorts suggested. I lived in Fredericksburg for 13 years, and with family in Williamsburg and DC, I can assure you, those are NOT easy drives for day trips. The other recommendations (are even further out).
The only TS that is really reasonable is the FF in Alexandria. I have stayed there and used it as a base, coupled with the Metro. Metro is very easy to use and reasonably priced. That is the best way to go! If you are unable to land a deal or trade into that resort, I would then suggest not using a TS and find a reasonably priced hotel for your trip. The hassle of commuting is simply not worth it in my opinion.
Also, the "bus tours" that are offered from the resorts, are decent to see the sights. You are unlikely to get to really experience them at any great detail. They hussle you around so that they can talk about ALL of the great places you have seen, but that's about it. Some of the attractions in DC Metro area require at least half a day. That is not a luxury you will get on Grayline Tours or any other similar bus.
Just my two cents worth . . . enjoy the city. It really is a gem!!
Yvonne