I second the Building Museum (their gift shop rocks!) and Rock Creek Cemetery, if only to visit the Adams Memorial (aka “Grief”).
A summer evening picnic at Bishop’s Garden, next to the Cathedral.
A DC United game, with tickets in Barra Brava’s section (that’s key…sections 135-138).
Bike to and walk around Roosevelt Island, visit Teddy Roosevelt memorial.
The National Arboretum and/or Kenilworth Aquatic Gardens (in July when the lotuses are blooming).
A nighttime monument/memorial tour.
Baked & Wired cupcakes.
Ben’s half smoke.
A weekend Beach Drive bike ride.
Climb to the top of Washington Monument (is that still possible?)