I'm heading to Williamsburg, VA soon (with stop in Mount Vernon). I plan on taking my drones with me. WIll I run into many issues? Aside from the usual don't fly in state parks, etc, not seeing much in way of regulations.
You can use a Drone in Virginia for recreational and commercial use, subject to FAA and local regulations. Official links and Virginia Drone Laws explained for residents and visitors, hobbyists, recreational, commercial and government drone flyers.
Just don't launch from Colonial Parkway or around Jamestown and I think you should be fine. Mount Vernon is doubly off limits because it's NPS property and within the DC FRZ, but downtown/Colonial Williamsburg is not a state park or anything so there shouldn't be any Virginia-specific restrictions. But I will say that the main stretch of Duke of Gloucester Street (the core of Colonial Williamsburg) can be pretty quiet because cars are prohibited during the day, so a drone might attract more attention there than it normally would.