That depends my good man, that depends. If you wanna hunt moose, caribou, deer, bear, I'd go for september. If you wanna hunt Bear, wolves, fox, coyote, and lynx, shoot for december or january. If you wanna fish the King salmon run (big fish above) mid to late june. red salmon(the best tasting in my opinion) early july. Silver salmon are good right now in valdez, but the run is getting over here in anchorage, so the second week of august. I'd personally come up for the kings. they fight the best, are the biggest, and that's about the best time of summer, it's day light 21-22 hours long
You'll probably have fun whenever you come up though. Right now I'm about 2 years into a lifelong hunting/fishing trip