Or, you might try Prince of Wales Island hunting. There are a number of B&Bs and lodges there which cater to sportsmen wanting to go after deer and bear. I suggest McFarland's Floatel, but that is only because I've known them for years. It can be reached with your own vehicle via the ferry system. Get there after September 1st and you can go after black bear also. Good fishing is available also, and the lodges usually can provide you with a skiff and gear to go out in.
Be prepared to do some climbing. The bucks are up in the high country, above timber line. There are lots of logging roads which will get you close enough so it's only a couple of hours to get where the deer are.
Since there are no brown bear on the island, a smaller caliber is entirely appropriate. I used a .308 for all the years I lived there. An island favorite is the .243, though I've seen folks out with .30-30s, .30-06, .22-250 and .25-06. Even saw a fellow with an H&R 12 guage using slugs. Jim Baichtal uses one of several caplock black powder guns (no inlines that I am aware of) almost exclusively to bring home his meat.
Bring rain gear. My experience has been that Gore-Tex isn't going to keep you comfortable. Go with loose fitting rubberized pants and jacket. Rubber boots are a must. I would wait until you get there and pick up a pair of "red rubbers" (Xtra-Tuffs). They have a sole which grips to anything, much better than vibram or the little knobby soles.
Good luck, stay safe and enjoy yourself.
-WH-