Go to whatever is on at the Kennedy Center Millenium Stage, their free performance space.
https://www.kennedy-center.org/whats-on/millennium-stage/
If you walk in every day life, Watergate to WH won't be hard. If you are used to driving everywhere, you might want to Uber one way.
Several Smithsonians require advance tickets now. I believe Air and Space, Natural History, and definitely Af-Am. But all the art museums are walk in and very nice. The Renwick Gallery is literally next to the White House and good for a quick stop. If you like colonial history or antiques, the DAR museum across the street from WH is great.
Walking back from the WH via the waterfront would be a lovely stroll. From WH, go south to Constitution, then West toward the Lincoln Memorial. You will skirt the Washington Monument and WWII monuments. At the Lincoln end, you'll go past the Vietnam Memorial. At Lincoln Memorial, head back north toward watergate along the riverfront. The waterfront path will bring you right back to hotel.