DNR (Dept of Natural Resources) has a range in Pickens and Abbyville counties. The Belton Gun Club has several range options up to 300 YD. The SkipJay range outside of Anderson is another option. Most folks are not comfortable allowing strangers to come shoot on their land. Some may shoot back in this area of the country.
Suggest joining a gun club will give you a place to shoot and allow you to meet local folks that have the deer propertys, dove fields, etc.