Sorry for the invasion of the AF forum by retired Navy but thought that I could help.
I live in the Pensacola area and am familiar with the area in question.
Some really great hunting is on Eglin AFB. They have closed some area's of the base in the last several years but there is still a bunch(couple hundred thousand acres)that is open to hunt.
You can obtain a license from Jackson Guard for $20. This will allow you to hunt everything in the base. You will have to obtain a state license also but being active mil it will only cost you another $20. Be sure to ask for the Military Gold license.
I hunt Eglin every year so PM me and I will be glad to elaborate on where to go inside Eglin. I primarily hunt hogs but have ran across some mighty nice deer in my trips around the base.
There are several gunshops in the area however one of them is strictly MSRP or better. I go in there every now and then just to look. The staff is knowledgeable and they have a bunch of the black guns,ammo,and some milsurp stuff. I look,feel,then buy somewhere else. I will be happy to give you the name in a PM.
Good luck with your PCS move. I did it a bunch of times in my 22 years.
You WILL fight....like you train !