Consider Baltimore’s Inner Harbor and the USS Constitution. Really, though, too bad you’re not flying into National, the airborn views are tremendous.
On top of the Kennedy Center is a great place to take pics. You should be able to get in here are free wthout going to a show. You would think that the Wasington Monument would be great too, but its windows are so small and thick pics don’t come out all that well.
Here’s a pretty decent tourist map.
Frankly, I wouldn’t waste time changing hotels. If you’re on a Metro line you’re close enough, even in Arlington.
There was a trolley service called Tourmobile that hit all the big tourist spots around the Mall. You could buy a day pass and and use it to get around on your own schedule.
You might want to look into renting bikes – you can bike along the Potomac all the way to Mount Vernon. Eh, maybe not with such limited time.
I always liked the Dumbarton Oaksgargens, but the museum is closed for renovations.
Just walking the Mall from the Lincoln Memorial to the Capitol is great. Also a great experience at night.
The National Zoo in Rock Creek Park is great, as is the Park. When I lived in DC the Park roads were closed to auto traffic on Sundays for walkers joggers and bikers. Don’t know if this is still the case.
See an IMAX film at the Air and Space Museum if you haven’t experienced IMAX before. If you’re into planes, check out the rest of it.
The Holocaust Museum is impressive, but depressing. I was so overwhelmed, I just had to walk out after a while – an incredibly powerful experience.
The National Gallery of Art has one of the ten best collections in the world, IMHO.
If you like architecture, a walk out west from Massachusettes Avenue from Dupont circle has lost of interesting buildings 00 this is “Embassy Row”.
Unfortunately a long weekend just isn’t long enough, even just to see all the great Mall museums, if you’re a real history dork. I lived there 12 years and there’s lots I didn’t see.
Some of my info might be dated as I haven’t lived there since '92.