Define "good" big game hunting. Are there places to go, yes. People from the states often forget that Alaska is BIG. Real BIG. While there are a lot of animals there is a lot of country for them to live in. In the valley there is the oppertunity to take Moose, Sheep, and Mt. Goats. For the sheep and the goats you are more than likely going to have to spend some cash to fly out.
For moose, while there are animals around it's not like the deer in the states. The valley is in Unit 14A, for moose the general season is 10 days long and there are antler restrictions (spike/fork or 50 inch antlers or 3 or more brow tines on at least one side). Just to the north is 14B where the general season is a little longer, 40 days ,with the same antler restrictions. For the 2005 hunting season there were 3547 hunters of which 576 were sucessful (about 16%) in units 14A and 14B combined.
I'm not trying to scare you away, but for the really good hunting in Alaska you have to get away from the crowds, which costs money. As far as the non-residents needing a guide, it is only for certain species. A non-reident is required to have a guide if they want to hunt: Brown/Grizzly bear, Dall Sheep, and Mt. Goat. There was talk several years ago of adding Moose to that list but that has not happened yet.
Now, if like myself you consider Good Hunting to be anytime you are outside with a rifle/shotgun/bow in hand then just about any community in Alaska has good hunting available to you.
Hope this helps.