One of the coolest things about DC is that despite being in the city, you can find nature all around you. Rock Creek Park, which runs the entire north-south length of the city, has some great hiking, biking and jogging trails that make you forget you’re in an urban area.
My favorite hike is the Valley Trail, which winds along Rock Creek from near the National Zoo to Maryland. That’s a long way, however, so I usually turn around at Military Road or head west to Fort DeRussy, part of the Civil War defenses of Washington, then back towards downtown. The fort’s earth parapets are still there, and historical markers describe how the fort was used to repel the Rebels when they raided the city. I sure wouldn’t want to attack or be based there.
On the west side of the creek is the Western Ridge Trail, which is hillier and more strenuous. It passes the Nature Center museum with some displays about local wildlife, Peirce Mill, one of the oldest buildings in the city, some funky, stone-crusted bridges, plus a lot of picnic areas. The trails have lots of access points, so you can go a long way or short.
The park’s part of the city’s popular imagination (just listen to the funk song about it,) but once you’re in it, you feel like you’re in the wild. That also means you had better bring snacks and water with you, as there aren’t shops. Bring a jacket, though!