what do you want to see in DC? Art, History? Tech? i mean, there is TOO MUCH to see in a couple days, but i fyou have a focus
Going to the top of the Washington Monument has a 'neat' factor still, but it takes a lot of time. However, on a clear day, you CAN see the temple from there.
the temple is a fun stop, but it sounds like you'll be there anyway.
The holocaust museum isn't what you'd call "fun" but it's very interesting.
There's the national archive, which has the COnstitution and the Bill of Rights (the originals) on display
I enjoy the American History Museum a lot, but along those lines there's also the natural history museum and the Air and Space Museum
The National Geographic Building isn't as impressive as any of the Smithsonians mentioned above, but it is more compact and has a better gift shop.
Mt. Vernon is a nice historical spot. most of the original layout and buildings are preserved and it's a beautiful spot.
And on that note, Gettysburg is in driving distance, and Bull Run is local, so if you want to see some Civil War stuff... (you've got to go further south or north than DC for most Revolutionary war or Colonial stuff)
There are half a dozen art museums including two branches of the National Gallery and the Hirshorn.
Then there's all the other monuments. these are mostly best if you have something you particularly want to visit. The best ones are the Jeffeson, Lincoln, Korean and Vietnam memorials. the War ones and the Lincoln Memorials are all clustered, so they're easy to hit in quick succession.
for just city life, you have your choice between the atmospheres of Georgetown (hipper, more modern, upscale) and Old Town Alexandria. Old Town is my preference, and it has, as the name implies, architecture still being used that's older than the settling of Utah, including the tavern the founding fathers used to hang out in. It's a waterfront district, so there's great shopping and dining, and the Torpedo Factory (formerly a place for manufacturing torpedos, but not an art gallery). My favorite used record store is here, and a really nice home made ice cream shop. Plus Hats in the Belfry, which is just a cool name for a store that sells (obviously) hats. Street Musicians hang otu a lot, not sure how many you'll see in the cold of February though.
I'd recommend some scenic places, but you're coming in Feb, no leaves. Still, Great Falls might still be impressive, it being the cateract that prevents shipping traffic up and down the Potomac. Skyline Drive won't be impressive this time of year.