I've lived in 16th Street Heights for a decade and would definitely walk all day and night, but that said it is a city. The area around Georgia/Kennedy can be a bit sketchy, though. Around Georgia/Upshur is lively and filled with stores. As you move west to 14/15/16 streets it's tree-lined residential.

As for metro, the nearest is probably Georgia Ave / Petworth. It's a 15 minute walk to Upshur, 30 minute to Kennedy. You might also try the buses. The 70/79 run between those intersections, the metro, and downtown all day long. It's somewhat rowdy around school getting out and at night, but otherwise a frequent city bus. The 52/54/59 on 14th Street is less rowdy and to a different part of downtown.