Welcome to the DC Area. Will you be locating in Maryland or Virginia? My own advise, avoid Maryland. Sorry to any local Maryland residents. We have more favorable firearm laws here in Virginia, especially if you should later seek a CCW permit.
Check Gilbert Indoor Shooting Range in Springfield, VA (703-550-8005). They're in Northern VA south of the Beltway at Exit 166A. Gilberts usually runs a PPC league. Not exactly IDPA, but if you're interested in PPC, check them out.
Here's another helpful site with plently of good info:
Washington D.C. Metro Shooter's Page
I believe
Shooter's Paradise has some IDPA events. But check with them. I may be confusing IPSC and IDPA events.