I like the Capital Alehouse, but it's more of a bar food/beer type of place. Bistro Bethem is supposed to be good, with a menu that changes frequently. There's also Foode ( http://www.foodeonline.com/ ), which is organic/locally sourced focused and was very good when I went there for breakfast.
If you go to Central Park (right off of I-95), there are a lot of chain restaurants there, but not a lot of local places.
309 William St, Fredericksburg, VA 22401