Most of the places to hunt around pensacola are Public management areas including Escambia river management area,Blackwater river management area and Eglin AFB are the three biggest and closest to Pensacola. Not sure about Escambia river haven't ever hunted but Blackwater and Eglin hold birds in places but with any public land the first few weeks there are tons of people in the woods. Birds are not everywhere but can be found with a little scouting.
I have lived in this area my whole life and have killed birds in two of the three places mentioned, but I have a lot of private land to hunt now but still get after those public land birds a few times a year. You can find maps and regulatons on the Fwc web site for the Wma and Jackson Guard.