It is very illegal in the district. It's also illegal in Maryland. You're good to go in Virginia though (but check local laws). If you're flying, I wouldn't even chance taking your gun. They've been known to throw folks in jail and throw away the key just for trying to check a gun at the airport if they know you've been in or through the district. I've been to D.C. a dozen or so times in the last few years - it's the only place I've felt absolutely threatened, afraid, and helpless to defend myself. I almost always stay in Virginia just to make sure my money doesn't go to the district, but I've never dared take my gun with me.
Reagan Airport is in Arlington, Virginia. Dulles is in Chantilly, Virginia, so you MIGHT be OK there. I would still be pretty wary taking a gun there. BWI is in Baltimore, so no go there. There isn't a major airport in D.C. proper. The problem is that Reagan and Dulles are administered by the Washington Metropolitan Airport Authority, which is a federal group. Both airports are federal property and are basically run by DC's finest, but there have been a few cases that clearly indicate that both airports are governed by the laws of Virginia, but that hasn't stopped them from arresting gun owners there for violating DC gun laws.