Cheap Things to do in at night that don't involve drinking in Washington, DC
The 11 Business Improvement Districts (BIDs) in each typically sponsors free outdoor movies, festivals, and musical concerts
The Kennedy Center's MyTix Program offers heavily discounted tickets to most performances for anyone under 30 and BravO Program opera tickets for anyone under 40.
Many fitness-related clothing stores in D.C. host free fitness classes and workshops. (i.e. Patagonia, Lululemon, Outdoor Voices, REI)
In Dupont, on the first Friday of each month, select museums waive their entry fee.
There are a number of open mics throughout the city & various comedy shows.
Most local bookstores in D.C. host a variety of free author talks where you can learn about upcoming new releases (i.e. Politics & Prose, Solid State Books, Lost City Books, Loyalty Bookstore, Busboys & Poets)
A variety of embassies & cultural centers host film festivals and art exhibit openings that are typically free. (i.e. Embassy of France, Embassy of Argentina, House of Sweden, Embassy of Austria, Mexico Cultural Institute, Korean Cultural Center, Cultural Office of the Embassy of Spain, Goethe-Institut Washington, Embassy of Finland)