There are really three Alaska's with different climates and different game animals.
SE Alaska is temperate rain forests with deer, black and brown bear, wolves and goats. Warm winters with generally little or no snow at sea level. No roads, just isolated towns connected by ferry. I include Kodiak as part of this, even though geographically it's separate.
Western and northern Alaska are true arctic country. Again, there are no roads. Caribou, moose, mountain grizzly, dall sheep (in the Brooks Range), wolves.
Then there is central Alaska which is essentially the road system between Anchorage, Kenai, Fairbanks, Tok. The southern part of this (south of the Alaska range - Anchorage and Kenai) has a climate much like the northern midwest. Hunting opportunities here are not much different than some of the lower 48. 90% of the population lives on this road system and by Alaska standards it's crowded. There is no really great hunting accessible by car. You can do OK but you're not going to see the great herds of caribou or bust a 70" moose on the road system. A lot of the game here is by drawing, etc. You'll find yourself chartering planes to hunt, but as a local you'll soon get to know people and find some great deals on that.
For my money, Kodiak or some of the small towns in SE are the best as far as hunting opportunity goes. With a skiff I can access some of the best deer hunting in the world, some fair elk hunting, goats and of course brown bear. As a resident I can hunt brown bear within the unit I live with an across-the-counter tag. And I don't freeze my @ss off during the winter.
Ketchikan is another neat little town. From Ketch you can catch a 30 minute ferry to Prince Of Wales (P.O.W.) Island and access about 1500 miles of logging road through some great deer hunting and the BEST black bear hunting on the planet. If you can't spot a dozen bears a day from the road during spring you are blind. You can also ferry up to the "ABC" islands (Admiralty, Baranof, Chichagof) and get brown bear hunting rivaling Kodiak. There are also goats available without a drawing in most of SE Alaska. Ketch has the same climate as Seattle, not too bad.
I haven't addressed any practical considerations like job opportunities or cost of living. Maybe you're "set" and don't need to worry or have a trade in great demand everywhere. The best job market and the lowest cost of living is in the Anchorage area. The cost of living is much higher off the road system and the further out you get the higher it goes, but generally wages are also higher. There is no state tax in Alaska and the revenues come from investments bought up by the state back in the windfall profits days of the big oil rush. Alaska residents are considered stockholders in these investments and you get an annual dividend per person of $1500-2000 a year which in my case is "guns and hunting charter" money.
May I ask what you do for a living? I may be able to steer you to something if that's a consideration.