DC is a great place to explore. But it is darned hot in the summer. We spent 5 days and really didn't cover all there is to see at the National Mall and the Smithsonian Air and Space Annex. We stayed at Cherry Hill in Md which seems to be far and away the most popular CG. They have a bus which takes you directly to the train station and that runs you right down to the Mall. You do not want to drive in DC.
The greatest altitudes I suspect you might run into are probably in West Virginia if you go that way. Just tall hills actually and nothing compared to the west.
BTW by going south and then west you can avoid the worst of the high altitude roads out west: take I-10 in other words.
We combined the DC trip with one to Boston, a couple of days to look at the historic sites there and from there up to Maine and Acadia NP.