WASHINGTON—On Wednesday, the day after government workers vacated federal buildings in downtown here, professional skateboarder Darren Harper got on Facebook and broadcast a message to his crew: "One positive thing about the gov't shutdown—spots at gov't buildings are now skateable!"

Where most people see ornate, neo-Classical federal buildings and sweeping stone plazas in this city, skaters see something else: opportunity, in the form of sturdy railings, low stone benches, ramps—ideal "obstacles" for skateboarding...