Battousai87’s answer is excellent, so not much to add, tho’ it’s probably possible to do almost any or all of the things you listed almost anywhere in Alaska. Right now the Kenai Peninsula is the hot spot for fishing, with Seward and the Homer area ranking high. Lots of fishing boats out of both, tho’ you can fish along the shores of many of the rivers and streams here (license rules do apply), but look out for the big furry fisherman with claws. Our grizzly’s tend to be territorial when it comes to someone infringing on their fishing territory. Would that count as a fight?
Hunting, not so sure, tho’ most of the guides that I’m aware of go out of the Talkeetna area. Some go more remote, so just depends on, one, what you’re hunting and, two, how “rustic” you care to go in the pursuit of your goal. I’m not a hunter, gave that up long ago before I even moved here, but seasons and permits apply, too. Moose season right now, at least I think it’s still going.
Photograph? Anywhere, and that’s no exaggeration. Catch a flight outta Talkeetna or anywhere in the vicinity to fly over Mt. McKinley, known here as Denali, or maybe a boat outta Seward or even Whittier, only accessible by one road or plane/boat, all year, and catch glaciers calving, whales breaching, etc. Actually, you’re as likely to see a moose wandering the streets of the city of Anchorage as you are in the wilderness, go figure, tho’ the wilderness tour in Denali Park is a must for photographers. You can also hike in but, well, how experienced are you with those pesty grizzly bears? Ha
Eat or drink? Hearing Salty Dog made me smile. Well, you might have to travel a bit to experience Native Alaskan foods, but even here in Wasilla (yes, the infamous Wasilla is my hometown) you can get food and/or drink of just about any culture or type you want. Anchorage is the best spot, tho’, most likely, if you want something more upscale, tho’ you can also stop and hoist a few brews at almost any of the local drinking holes. You’ll certainly find locals there, tho’ some of the lakes and recreational areas might be your best bet if you’d just as rather leave the fighting till later.
Oh, and did I mention that, yes, you can see Russia from Alaska, you just have to travel a bit to get to that spot.