Things to do in DC:
All the main museums are free.
It’s worth a day on its own walking from one end of the National Mall to the other - you have the Lincoln Memorial at one end and the capitol building, senate and national library at the other, with museums on either side as you walk, and the Washington Monument. The Air and Space and the Natural History museums are probably the best two. A random decent one is the Postal Museum - an interesting history, a Unabomber exhibit, and lots of rare stamps.
Not that far away (walkable) are the White House, Iwo Jima monument, and the Jefferson monument, all must see.
Arlington Cemetery (the military cemetery) - over the river (get the subway there). Very moving, thousands of graves including some presidents (e.g. JFK), and a few monuments like the tomb of the unknown soldier.
Seeing the Nationals - if it’s an evening game check the subway times, annoyingly some of the lines shut early so you can get stranded if you’re staying on the other side of the city. The stadium is great, you’ll have a good view wherever you sit.