I lived in Fort Mill until recently. There are routes in Fort Mill that aren't bad. Look for York County bicycle route signs. But I would look more at Rock Hill starting at Main Street. You can ride out to Brattonsville or Chester Airport. If you want to ride longer than that, there are routes to Kings Mountain. Most of these have very little traffic.
Rock Hill Bike Club has rides on Monday evening and Saturday morning, leaving from Wells Fargo parking lot on Main Street.