I spent two summers (1977 and 1978) living in Anchorage, Alaska when I was a kid while my dad was managing mining exploration projects in the Alaska and Brooks Ranges. I probably won't be much use in telling you specific restaurants or attractions, but what I will say is that the best parts of Alaska for me were just the trips driving to various places. We would drive for an hour or so, stop on the side of the road next to a river and go fish for an hour or two or hike up a hill to see what was around. The wildlife we saw, the fish we caught, etc. was amazing. It is just an amazingly beautiful place pretty much anywhere you go outside of the big cities.
One of the really cool things I remember as a kid was driving out to Paxson, staying the night somewhere out there and then coming back riding the car ferry from Valdez to Whittier through Prince William Sound. We saw tons of glaciers, killer whales, dall porpoises, bald eagles, etc. Driving and hiking around off the highway, we saw moose, bears, dall sheep, and caught all kinds of fish. I say all that just to say that if you enjoy great scenery and wildlife, you don't have to go somewhere special or spend a lot of money to get to it in Alaska, just get out of the cities and drive the roads and hike in the parks.
It is on my bucket list to go back with my wife and show her a lot of the places she has had to listen to me rave about for the last 30 years. I would love to make it out to Katmai, but mostly I just want to drive around to places like Denali, Homer, Seward, etc. and maybe ride the Alaska Railroad.
If you do happen to be hiking out there and hear a guy walking along humming Christmas carols in the middle of the summer, it might be me reliving my childhood. My dad would send my brother (11-12yo) and I (7-8yo) out to hike up a hillside (to burn off some energy during long drives). He told us if we made a lot of noise the bears would hear us coming and leave. He suggested singing songs. Well, the only songs my brother and I both knew the words to were Christmas carols. So we spent two summers hiking up many a hillside in Southern and Central Alaska while belting out Jingle Bells, Santa Claus is Coming to Town, etc. in the middle of July. I am sure it was hysterical to the locals to listen to with our Texas accents.