Haci Bekir Turkish Delight
My recommendation would be Cenan's, a Turkish bakery/cafe/store at 122 Branch Road in Vienna. (Phone: 703-242-0070) I've shopped for simmit and cherry jam there, but I haven't shopped for Turkish Delight specifically.
When I did a search to give you Cenan's precise address, I discovered a web site that listed other Turkish grocery stores nationwide. Some of the stores will do mail order business and there are three additional retail stores in the metro-DC area. Here's the link to that web site: http://turkishconnection.com/food2.htm