If you stay in the SW Waterfront area you will likely be within 1 mile of the National Mall and all it has to offer. It would take a full day to just see all the monuments let alone go inside the museums. All of which are free entry. My favorite is the Museum of Natural History.

The long, grassy National Mall is home to iconic monuments including the Lincoln Memorial and the Washington Monument. At the eastern end is the domed U.S. Capitol, and the White House is to the north. It's also flanked by Smithsonian museums, and its lawns and pathways are often crowded with school groups, joggers and softball teams. Nearby, the Tidal Basin reservoir is known for its blossoming cherry trees.

One of the things I love about the DC area are the miles upon miles of black top, bicycle dedicated paths (not on the road but separate paths) between DC, VA, and MD and some of the most beautiful parts run through Rock Creek Park. Just driving through the parkway there and going to a restaurant somewhere in Woodley Park or Adams Morgan is a great activity. Enjoy the scenery!

Many people don't know this but, Virginia is chock full of vineyards. Just an hour-ish outside of DC you can find several. If you are staying for more than just the wedding and museums and monuments aren't your thing, consider renting (or hiring) a car and spending the day in the Virginia countryside visiting a few vineyards. You won't regret it. The drive is beautiful and wines are great! You can find some trails at the link I provided.