Depends on location. In SC, you can't legally target shoot on public/government lands. In my area DNR DOES maintain a free shooting range open to the public, but if you're just in the woods at random, you can only shoot a firearm in the process of hunting.
You can naturally shoot on your own property though. My brother for example lives on a dirt road in the middle of the woods - no other houses around and almost no traffic (he might see a car go by once an hour).
On the side of his yard we made a short little pistol lane with a dirt backstop, and we'll just shoot pistols in the yard quite a bit. Beats going to the crowded range (I wouldn't mind the range, but sometimes I've waited an hour or 2 for a table to open up, and once the range goes hot you're going to be waiting 30-45 minutes before you have a chance to go change your targets, which for me really hampers shooting for groups or testing different loadings.