The obvious next stops are Georgetown to the west or the East End to the east for dining, shopping, and nightlife a ten–fifteen minute walk or a $1 Circulator bus ride from Foggy Bottom, and south to Potomac Park, the Tidal Basin, and the Mall.
Slightly less obvious is to head north to Dupont Circle, where the nightlife and dining is a bit more local, and a bit more fashionable.
Arlington, home to the famous cemetery, National Airport, and more downtown dining and business, is just across the bridge, and is easy to reach via the Blue/Orange lines or by bus or taxi.