If you haven't visited DC before, make sure to visit the hits: Washington Monument, Lincoln Memorial, The White House, all the museums, basically anything on the National Mall.
For all your shopping needs, pretty canals to walk along, and cupcakes.
The National Cathedral has a pretty garden and a green lawn perfect for a picnic.
Old Town Alexandria is a cute little area by the water with cobblestone roads and plenty of shops and restaurants, especially along King Street. The jambalaya at the Fish Market Restaurant was great when I tried it.
If you want a nice low-hassle walk/hike in nature, this is a solid spot near DC.
If you don't mind driving out an hour or so, make sure to visit Shenandoah National Park for great views. You could hike if you want, but you can also just drive along the Skyline Drive to visit various overlooks.