Ohio operates two different levels of outdoor ranges. There's a fee (day or yearly permit) chargedfor the Class A ranges. Nearest two of those to Columbus would be at Delaware State Park and Deer Creek State Park. You can get the range permits wherever hunting/fishing licenses are sold.
The Class B ranges are no-charge, but they are absolutely bring-your-own-everything including target stands.
There are three indoor ranges around Columbus. Blackwing Shooting Center is west of Delaware, The Powder Room is in Powell, and there's AimHi in New Albany. Personally I like Blackwing the best of those three by a wide margin.