Welcome to Virginia, even though you're moving to Arlington... which is almost an extension of Washington, DC.
I'm a member of two local ranges. One is the Arlington-Fairfax Chapter of the IWLA (Izaak Walton League of America) which is located at the bottom southwest corner of Fairfax County just a little above Manassas. We have 140 acres with a covered 100 yard handgun/rifle range, a skeet and trap range, archery, a stocked fishing pond, and camp grounds. The other range I belong to is the NRA indoor range in their national headquarters building in Fairfax. Both of these ranges are excellent. There are other ranges around our area as well. You won't have any problems finding one to go to.