IMO DC is still a unique and pretty city even if you can't enter federal government attractions. You can still enjoy the wide streets, parks, building exteriors (will the monuments be lit up at night?), Georgetown, etc. With any luck, the city will be uncrowded. Plus the Willard is a special hotel.

If the tickets are nonrefundable and your airline isn't offering a waiver, there isn't much choice. Driving to NYC would be miserable.

You might want to spend part of a day away from DC itself, perhaps at the Baltimore Inner Harbor and Acquarium or in Annapolis, a charming historic small town but check whether you can enter the Naval Academy Grounds. This would require a rental car. The eastern shore (of Maryland) can be pleasant too, but it's far.

ADDED: I like the idea of Old Town Alexandria. I don't know what interesting nearby state parks are in Virginia. Also farther away in Virginia, there's Charlottesville (state capital), the Shenandoah Valley, Roanoke (are the attractions federal?), and the SkyLine Drive. Pipestem and Blackwater Falls are good state parks, but again the distances are too far.