It's quite a way from West Palm (90 minutes?), but until you are able to find something closer you are welcome to shoot at the Port Malabar Rifle and Pistol Club on Saturday mornings. The shooting starts at 9am sharp, but I recommend you be there by 8:30 at the latest to set up and learn the ropes. You sign in at the front gate and they will give you directions. Cost is $5. Hope you can make it.
http://www.pmrpc.com/