Maybe it’s one of those things that everyone knows about, but it bears repeating. The Kennedy Center has free shows (reserve a ticket online) Wednesday through Saturday at 6 pm at their Millennium Stage. The schedule is at this link. That is the long area out in the waiting area by the giant head of John F. Kennedy.
The shows are also livestreamed.
In the US (and in 120 other countries), you will see these little boxes with free books. They are part of Little Free Library, a non profit organization.
I have seen some towns where they have boxes with free tools or free food. I like this idea.
When you have seen everything else you need to see in DC as a tourist, try these things (or look at my list of walks):
Listen to the Drum Circle at Meridian Park, Sundays at 3 pm. It’s free and loud.
Visit the Library of Congress. Free but timed tickets required.
Go to the National Harbor and the National Wharf. Free areas with restaurants and outdoor activities.
Visit the oldest farmers market in the USA in Alexandria. George Washington sold stuff at this market… Free, only on only Saturday mornings 7-12 noon.
Shop at Eastern Market. On the weekends, there are also outdoor stalls with art, fresh vegetables, etc. The market is over 130 years old. Free and on capital hill.
Take a water taxi from Georgetown to Old Town Alexandria or Mount Vernon or to the National Harbor. It’s a cheap way to get a boat cruise.
Go on a wine tour. There is one right in DC and there are many about an hour or two from DC. Read about all these great places from this Washingtonian article.
Harpers Ferry is one of my favorite day trip destinations from DC. Go for a hike up the other side but make sure to learn some history in the town. Free.
Hike or drive in the Shenandoah. You might go there to visit the famous cavern, but driving along Skyline Drive is fantastic too. Or stop for a hike. Fee for entering the park. Or buy a year pass.
Take the train to Frederiksburg, Richmond, Baltimore, or Annapolis. All within a two hour train ride.
Watch a comic or movie at Arlington Cinema and Drafthouse (this is a historic, if tired, art nouveau building from 80 years ago). Price of tickets, but you will likely not see other tourists here.
Take a paint and sip art class. See this list. Or a cooking class or some other class. Check out this site for more info.
Go to a Korean spa like Spa World or King Spa, or go to a hammam. Scrub yourself away to another world.