A great place for a deer hunt in Alaska is found on Kodiak island. The deer are plentiful and really have no natural preditors. The limit is two. A good contact to make your hunt a bit easier is to contact Andrew's Air to fly you out to the forest service cabins that are availiable. Again, you want to sign up for them well in advance. You can do this online.
In addition to your hunt there there is year round fishing of halibut, salmon, and dolly varden. Once you shoot a deer you really need to be aware that once your take a shoot and kill a deer its like ringing a diner bell for a bear. They know that there is a gut pile for desert that they can snack on nearby. In the state of Alaska you can shoot a bear in self defense but you have to skin it and give the hide to the state DNR:)