No need to stray too far from the city! DC surprisingly has a few green places within the capital and all you have to do is look for them! Here are the closest spots in DC.
If you like hiking near the water, head to Virginia! There are a ton of great spots to see waterfalls, lakes, and panoramic views.
Maryland has a ton of hiking near DC on the Appalachian Trail! There are so many that offer great panoramic overviews of valleys! Check them out!
Harpers Ferry is where West Virginia, Virginia, and Maryland need, and it's not too far from DC! There are a ton of great hiking trails surrounding the city!