City code 10-7-4(d): “Bicycling on the sidewalk shall be prohibited in King Street/Union Street Commercial Zone. This zone is on King Street, from West Street east to the Potomac River, and on Union Street, between Prince Street and Cameron Street.”
Note though that state law 46.2-904 says “Signs indicating such prohibition shall be conspicuously posted in general areas where use of roller skates and skateboards, and/or bicycle, electric personal assistive mobility devices, motorized skateboards or foot-scooters, motor-driven cycles, or electric power-assisted bicycle riding is prohibited.” IMO the area where biking on sidewalks is not well signed, so you might have an argument if cited. Also it seems that Alexandria (inadvertently?) exempted e-bikes from the sidewalk ban.