There aren't any trap clubs real close. Port of the Islands is probably the closest, south and west. I shoot at Sarasota, for me it is about 80 miles north. From Fort Myers it is about 50-60 miles north. A really nice club.
Port of the Islands is 50-60 miles south of Fort Myers, Sarasota is 50-60 miles north of Fort Myers. I prefer to go to Sarasota , the drive north on Rte 75 is very easy and the club is about 5 mins off of Rte 75.
I live on Sanibel Island and I have a 20 mile drive to Rte 75 and then 50 miles on 75. Takes me 1 1/2 hours to get to Sarasota. I go most week ends and enjoy the shooting there. During the winter they have registered shoots, Big 50 shoots and doubles marathons. Check their website for the schedule.