Not an expert by any means, but some thoughts:
--We stayed a Residence Inn near the ... I want to say Federal stop? If you look on google maps, it'll be several large blocks south of the main Smithsonian area and around the corner from a metro stop and a Starbucks. Parking was annoying but that will be true anywhere (tiny garage, but doable), and a queen suite was about a hundred bucks. It included a hot breakfast buffet. But we were definitely in off-season, the dead of January. Actually, I also stayed there again in June of last year, come to think of it, and I think I still paid under $200 a night for a pretty big room/suite. The walking distance to that metro stop is very nice.
--Prepare for almost as much walking as WDW, even with metro stops it's a LOT of walking. There isn't a particularly close metro stop to the Smithsonians, for example. You may save yourself a few blocks but you'll lose that time getting down to the actual platform and waiting.
--Keep in mind much of the town in the area of the Smithsonians simply shuts down on the weekends. Even the Starbucks around the corner from the Residence Inn was closed on the Sunday we were there. So when you are researching quick eats near the hotel and you see something like a deli that seems promising, be sure to check their hours. You may discover they are not open on weekends. We had a car on my first trip and ventured out to other neighborhoods for dinner; on my second recent trip we took the metro to another neighborhood for dinner.
--Study maps of the metro system ahead of time, it'll make it way less confusing when you're actually there trying to figure out which line and direction you need.
--Make dinner reservations for TS, you will need them.
Oh, and there are really good fried oysters to be had there.