There's a bunch of parks throughout the metro area that are somewhat escapes to nature to varying degrees. Glover Archibald Park, the parks/reservoir just north of Sibley Hospital, Jones Point, and Dyke Marsh Wildlife Preserve are all places I've gotten to without a car or bike.

The major trails match up reasonably well on Google maps. You could also walk in the farther north parts of the park where it's more one winding trail and less a vast forest -- just pick where you want to enter the trail and where you want to exit.

I've walked Mass Ave before from Dupont Circle to Maryland. It was pretty fun! I enjoy picking a street and walking it in general.