I cant say for immediately around Fredericksburg, but about 50 miles south at Kings Dominion (Doswell Va) is a decently rated KOA, pricey for me at about $80 a night, 20 miles farther south in Ashland Va is an Americamps, right by the Interstate, easy on and off, about $60
Or if you are in no rush, Lake Anna State Park, 40 miles south of F'burg but not right along I-95.
Nice sites, w&e around $40.
Lake Anna Stete ParkThese are all off of 95, not along 17
East of 17 40 miles south of F'burg is
SWestmoreland Stete Park, I have not been there so cant say anything about sites.