Consider Hotwire and Priceline.
www.betterbidding.com is a good site for seeing what hotels others have gotten, both in DC and surrounding areas (you can also ask questions). Will you have a car? You'll likely have to pay for parkingin most areas in or adjacent to DC, though maybe more in DC itself. On our last coupleof visits, we stayed in the Rosslyn area of Arlington, immedaitely across the Potomac River from DC, and took the Metro rail into DC.
Note that terms like "Capitol Hill" are used by some hotels even when they're not actually in the Capitol Hill area (which I don't believe has legally-defined borders, anyway). Some parts of Capitol Hill you wouldn't want to stay in, anyway. I lived in the area for a few years and would actually consider Dupont Circle partof downtown, but hotels may not. I'd look up reviews of the hotels you're considering, and maybe add Arlington to the mix. L'Enfant Plaza is a bit of a walk to downtown restaurants, and probbly not something you'd do late at night, but you can get there by taxi or Metro. It would help if you gave an idea of your budget. If budget is no object, I'd consider one of the hitoric grand dames, such as the Willard (hosted Civil War conferences), Hay-Adams, etc. Smithsonian museums cover a fairly wide area, but the very cloest hotel to the Air & Space Museum (the origiinal, not the annex out by Dulles Airort) and Holocaust Museum (not Smithosnian, of course) is probably the L'Enfant Plaza Hotel. As noted, there aren't as many restaurants, etc. there as there are downtown, or Crystal City or Rosslyn.