Ben’s Chilli Bowl is a must. For a nice dinner that’s not cheap but not, like, 10-year anniversary nice, try Jaleo, a tapas place on E and, maybe 7th. It’s a great place to just hang out and eat and shoot the shit with a couple friends.
Of the Smithsonians, Air & Space is the most popular museum in the world for a reason, and Udvar-Hazy is also awesome, although probably both on one trip is too much unless you’re serious aerospace or space geeks. Other museums I’d recommend are American History and, if you’re interested in art, the Freer. It’s a weird and fantastic collection of both 19th century Western art (esp. Whistler and his contemporaries) AND all sorts of Eastern art from various time periods. Whistler and his group were very influenced by Eastern art, so when Charles Freer started collecting those guys, he got into Asian art as well.
Also the Phillips Gallery (a private museum in Dupont Circle) has an excellent collection of both Impressionist and Modern art, as well as older stuff, which is exhibited to try and highlight how the masters influenced modern artists.
I can’t agree with the recommendation for the Spy Museum. It has its points of interest, but mostly I found it mediocre – which is too great a sin to overcome for a museum that charges admission (not cheap, either!) in a town that has so many excellent free museums.
Definitely try to plan your day’s itenerary. The Smithsonian museums on the Mall are Metro accessible, as are the private museums cormac mentions. The Phillips is a bit of a walk and it’s better to drive. Udvar-Hazy is out in the boonies and you need to drive.
Parking in D.C. is actually pretty reasonable for a big city. There’s little parking down on the Mall (not none). But there’s plenty of parking two blocks off the Mall in the business area – the best thing to do is the Metro, but if you need to drive for some reason you can park in one of the garages – it’ll be $10-12 all day on a weekend, $20 on a week day. It’s also not too hard to find street parking if you’re willing to be patient, but those spots are usually two hours, so if you want to spend a whole day it’s better to either Metro or find a garage.