I spent 22 years in Alaska, most of that time was spent shooting for the Alaska National Guard Shooting teams.
During the summer there are at least 1 hp match a month, and winter there are small bore matches. There are several pistol matches, both combat and bullseye. If you're in the Anchorage Bowl you can find some sort of match dern near every weekend.
Google the Alaska State Rifle and Pistol Assn. Also chech the NRAs Comp Shooting mag (brain fart, cant think of the name), each month it list several matches in Alaska.
The Anchorage Bowl, is shooter friendly as far as compition shooting goes.
For public ranges you have the Rabbit Creek Range in south anchorage and the issac walton ranges in Birchwood. Both use to post the list of matches in the area. Lots of good gun stores in Anchorage Also.
If its big game hunting in Alaska you are gonna be disapointed. Its pretty much a rich man's sport anymore, you're gonna have to fly out unless you live in the bush. Fishing and duck/goose hunting is great though.