There are fish to be had from the lower Chesapeake Bay through the Outer Banks of North Carolina. The Bay is almost unflyfishable from shore, especially during the winter. Your best bet would be the Outer Banks. From what I've seen and heard in my limited fishing there, it is possible to catch fish on the fly from shore, but they tend to be out a bit far due to the lack of steepness to the beach. The fish also move a lot and blitz the beach occassionally. Many folks cruise the beach looking for birds and crowds of fishermen -- not great if your a fly fisherman. If I were going to Hatteras at theat time (I wish I were... ) I'd bring surf tackle as well as the flyrod, or pony up the bucks for a charter.
Regards,
Eric Lund