How fast do you need and roughly where in DC are you staying? In addition to the Tesla store/gallery chargers, there are lots of Level 2 options inside the Beltway, several of which are in/near hotel parking garages, according to PlugShare. If you're planning to charge overnight, L2 should be plenty to get you back to Newark DE or Southern MD the next day. But if you'll only be in DC a few hours then the superchargers are probably your only viable option.
I'm familiar with a few options in northern VA. I know a number of Model S owners used L2 chargers near hotels in Crystal City during a local event in February, and I know of a Residence Inn in Ballston that has L2 charging in its garage. Just a bit outside the Beltway and just south of Tyson's in Merrifield VA, the Mosaic District has several free L2 chargers near a Hyatt House hotel.
By the way, Tyson's has at least one NEMA 14-50 outlet in addition to its HPWCs in the Tesla parking area. Also, I agree with JST and recommend calling the store ahead of time if you want to be sure of charging there.