I was stationed in P/Cola for 4 years. I did a lot of hunting and I took deer every season. Since I lived out on Mobile Hwy just east of the Bama line I hunted Perdido River WMA a lot. It's a quota hunt but I was always able to get firearm and muzzleloader permits for it. Blackwater can be good and there is also Escambia River WMA. Escambia River is hard to hunt if you don't have a boat.
Eglin has a lot of land and a lot of deer. I always got a base permit but I didn't hunt it much. I met a guy that lived north of Crestview and he had a bunch of property. He let me hunt so if I was headed that way I'd rather hunt the private land and not be aggravated with all the rules for hunting the base.
One thing to keep in mind about hunting around P/Cola is that the deer are a whole lot smaller than you're used to in WI. The biggest buck I saw taken in the area was shot by my Dad on that private property and it weighed 155 live weight. So don't be expecting big deer. Also they don't have the minerals for big antlers for the most part. If you see a 5 or 6 pt you better consider taking the shot. The cover can be really thick and even though it is deer season there may be snakes out. I saw both cottonmouths and diamondbacks while I was deer hunting.