We haven't been been to Williamsburg in a few years, but when we last went we stayed in the "1776" hotel - can't remember the chain (Holiday inn, I think?). Very nice and peaceful, away from the crowds, and a very short drive into Williamsburg itself. Has a full-service restaurant on site. Jamestown isn't that far away, for a nice side-trip.
We live in the Washington, DC area (Northern VA), and I second the metro hotel(s)! Take the metro, take the metro, take the metro! Both my husband and I grew up here, and we avoid driving into town like the plague! You can actually do metro cheaper than $6; I think that's the day pass, which probably is easier if you'll be travelling around on the system. I can second the Embassy Suites across from metro in Alex (King Street Metro). Old Town Alex is absolutely wonderful, but my husband is a p.o. in Alex so I'm naturally biased!
We frequent the Smithsonian and other museums because our daughter is an Art History major here. The food is indeed very expensive, at times the quality and selections may be a bit off, and it can be extraordinarily crowded in the museum food areas. The security check lines can appear long on the outside of the museum as the guards are thorough, but they're usually well-staffed and move surprisingly quickly. That is, as long as people don't pack what they shouldn't - last time we went an elderly couple had what they described as a very small pocket knife in the wife's purse. They told the security guards about it before they went through the detectors, purse check, and sweeps, but it turned out to be about 6" in length, folded, and the ensuing argument (what do you mean we can't bring it into the building?) really slowed things down. It's amazing what people will bring with them, even with the added security being no secret.
The area is beautiful in the spring and fall, and it's less crowded. Summers here can be like Disneyworld - hot and crowded! Hope you have a great trip!