About Central Virginia Family Medicine. Central Virginia Family Medicine is a group practice with 1 location. ... Central Virginia Family Medicine Office Locations. Central Virginia Family Medicine. 2301 Fall Hill Ave Ste 302 Fredericksburg, VA 22401 (540) 370-4370. Monday : 9:00 AM - 5:00 PM: Tuesday : 9:00 AM - 5:00 PM: Wednesday : 9:00 AM ....