Sticky Fingers is absolutely amazing! Definitely a must do.
If you go on a day when they have vegan soft-serve ice cream, you have to get some!
<<<drooling now thinking about the oatmeal creme pie things they have (can't remember what they're actually called)
It's a little touristy in the neighborhood by the Affinia. There are a couple of Hyatts in the area, but I'm guessing you mean the one that's like right next door.
It's a snap to get around most of DC on the Metro though, and it's surprisingly clean and safe.
Some of my favorites from DC:
Soul Vegetarian, on Georgia Avenue, across from Howard University. There is a restaurant and the owners also have a small shop, Everlasting Life just a few doors down. There's a takeout counter in the shop, but there's usually less variety than at the restaurant (where there are also some seats). The BBQ seitan and the carrot salad are fantastic! My sister (who lives in DC) could subside on their mock tuna salad I think. And desserts...mmm.
If you get off at the Howard Metro stop, it's still a pretty good walk, but not bad if it's a nice day.
Busboys and Poets: http://www.busboysandpoets.com/
Very hip and cool, although some may criticize that it tries too hard to be.
Usually all sorts of neat stuff happening there. Vegan friendly menu.
This place http://www.javagreencafe.com
is sis' favorite, I think. Quick food, a bit pricey, but very nutritious and yummy.
There's a really good fast food Indian place too, called Naan and Beyond, if you need a quick bite one day. There are a couple of locations, one's in the food court (I know, I know) at the Shops at National Place. It sounds silly, but the food is delish!
If you have time to do the touristy stuff, you'll never run out of ideas. The Spy Museum is a riot! The Air and Space Museum (the part in Virginia) is fantastic. The Library of Congress, the National Archives, and of course, the Mall have all warranted repeat visits for me. The Holocaust Museum is very interesting as well, although I'm not sure I'd want to go again.
I'd never want to live there again, but it's a very fun place to visit.