It's hard to classify things as "must-sees" since one man's "Must See" is another man's "overhyped tourist trap." But here are my tips:
If you are in any way interested in airplanes and space, the Udvar-Hazy annex of the Air and Space Museum is very worthwhile (there's a bus connecting the two at the A&S museum downtown, as U-H is way out near Dulles airport). It's as close to a must-see for a space/airplane technology person as I can think of.
I can HIGHLY recommend eating lunch in cafeteria-style Mitisam in the "new" American Indian Smithsonian. The food is excellent and, for a Brit visitor, it might be fascinating to see the variety of truly "American" foods on offer. I didn't personally find the museum that interesting (IMHO not to the standard of the others) but the food was amazing.
Off the beaten track places that I liked while living there are:
- National Botanic Gardens (between the Capitol and Native American Museum), small but an interesting spot nonetheless.
- Eastern Market
- Tidal Pool (nice walk/picnic spot)
Best to visit at dusk/after dark:
- the WWII memorial (much, much more stunning at night than during the day - really, I feel this way about all the war memorials: Korean, Vietnam, etc)
- Lincoln Memorial
General advice:
If it's hot outside (and it likely will be) the Zoo can be a long, painful visit, and the animals might not be very active/entertaining. If you've got a misty, drizzly morning, that's actually the best time to visit the zoo in the summertime if you can stand it. Beware: It's a big zoo and the walk to the Metro after a long visit can be maddening! My other tip is to get off at Cleveland Park and walk DOWNHILL to the entrance to the Zoo, rather than getting off at Woodley Park and walking UPHILL!
Proper "downtown" can be really dead after 6pm, when 90% of the Feds have gone home to the 'burbs. Unfortunately, proper downtown is also closest to the main bit of the Mall, so if you're looking for somewhere to eat after leaving the Smithsonians at 5ish (particularly on the south side of the Mall: A&S, American Indian, etc) you might be walking a while before you find somewhere. The best places to get good food IMHO are near Penn Quarter (Metro: Gallery Place/Chinatown), Dupont Circle, and near M/Wisconsin in Georgetown. Tom Sietsema's reviews in the Washington Post are an invaluable source of information for all cuisines, all budgets, all areas.
Crystal City is often thought the provide the best combo of good value hotels with proximity to a Metro stop. Other areas to consider are Rosslyn, Silver Spring, and Bethesda - which have nice little semi-urban centers in their own right.
