The Main Avenue Fish market is a brief walk from the L'Enfant Plaza Metro stop and something most vistors never find. It's actually a pretty easy walk from the mall as well.
If you want industrial/underconstruction/slightly slummy head over to the waterfront near the new Nationals Stadium.
Georgetown, if you get off of the main drag (M Street) has some great architecture and some lovely walking trails along the canals that would give you either street life or serene water scenes. M Street is your typical higher end shopping district, but if you look closely you can find some interesting images. If you want a tattoo I recomend Jinx Proof, I got my half sleeve of cameras done there
If you want to see Graffitti then take the red line out toward Shady Grove (only do this during the day as it can get a bit sketchy).
"China Town" is only worth photographing for the gate...there is pretty much nothing "China" about it any more.
For an iconic hole in the wall there is Ben's Chili Bowl on U street (I've been meaning to photographic this place for some time).
You can also check out Eastern Market (Eastern Market Metro stop on the Blue Line, at the stop head toward the school and you'll find it in a couple of blocks). On the weekends there are craft/antique/fresh produce vendors to compliment the market.
I live just across the river in Old Town Alexandria so feel free to ask me anything.