Clan Vidivici (me & the Mrs., two teenage boys) spent two weeks there on vacation in 2011--about 2 weeks before the earthquake that damaged the Washington Monument. Oh, yeah--DC was also experiencing record-high temperatures. Yeesh.
Absolutely. Smithsonian. (And, they're all free admission!) If you're into spacecraft, the Udvar-Hazy center is the closest thing to a cathedral you're ever going to walk into.
I cannot recommend highly enough the Spy Museum. Plan on spending a day. It is by turns silly, and amazing, and sobering, and scary, and full of "huh!"
We made day trips to Monticello and Mt. Vernon that we enjoyed. The museum at Mt. Vernon was pretty good. I came home from that trip with a deep appreciation for Thomas Jefferson. Learning more about him and getting a feel for his life by visiting Monticello, and then standing in the Jefferson Memorial and reading his most important words left me deeply contemplative.
The National Zoo was a disappointment, especially if you've seen a really fine one like San Diego or--surprise!--the Chaffee Zoo in Fresno.
One bit of advice we got that was definitely worthwhile: on your first full day, take a touristy tour-bus tour of DC. You get your bearings, you have a goofy kind of fun, and you develop a list of things you didn't know you wanted to see. DC has lotsa trolly tours. We took one that started and ended at Union Station (quite a sight in itself) and the took the DC Duck--a military-surplus amphibious troop transport. Both were totally worth it.
One thing we did not get to do was get a tour of the White House and Congress. You have to get reservations for those at least three weeks in advance, and we didn't plan this trip that thoroughly, we just sorta winged it. That was disappointing. Check their websites for requirements.
Enjoy your trip!
“To day is a good day to die for all the things of my life are present." --Crazy Horse, prior to the battle of Little Big Horn