Norfolk has a Farmer's Market that is pretty good - The Five Points Community Farm Market. I haven't been in a few weeks, though so I don't know what they have right now.
The main location is the the "Five Points" neighborhood on Norview Ave and Chesapeake. They are opened 10-2 Mon-Sat I think. There is also a nice, newer location downtown just outside MacArthur Mall opened Th-Sat 10-2
Williamsburg's Farmers' Market is suppossed to be really nice and Newport News also has one that I've seen ads for.