Ah Axis deer, a subject near and dear to my heart. I love axis deer both as a game animal and as table fare, something I cannot say about the more common whitetail deer. If they were free ranging in the areas I can hunt I'd never hunt whitetail again.
The Brady Ranch in FL supposedly has the largest herd of axis in the world. Like most all other places to hunt them these days they aren't free ranging but they are on a quite large piece of ground there and the fence isn't likely to come into play in your hunt so for all practical purposes they might as well be free range.
I'm not aware of anywhere else other than in TX where you might find that to be the case. Most all ranches that offer more than the cheap sheep and goats will offer axis. While I'm not sure the names of all the places I know that NY state, Vermont and PA have preserves with them. I'm not aware of any place in the Carolinas with them but several of the primarily hog hunting places in TN do.
Given the same living conditions you'll find axis a more wary deer than whitetail and the fallow as much as I enjoy hunting them a bit less wary than the whitetail. I've hunted where all three were available and found that to be the case at least.