Anthology apartments are near the Navy Yard in Southeast DC, so you can visit SE DC and then come home to a place closer to more awesome neighborhoods including NoMa, Capitol Hill and the Atlas District.
The Navy Yard Metro stop. Not awesome, per se, but lets you get here pretty easily by train.
Casual spots for a beer, like Bluejacket brewery, to the slightly higher-end cuisine of Osteria Morini, there’s a wide range of stuff to do, see and eat over here. Check the map for more.
Venues for entertainment, including Yards Park and Nationals Park. You may want to venture towards the Potomac and explore this new/old part of DC.