I returned from a 12 day holiday in Alaska yesterday. If you haven't visited the "Last Frontier" yet, I highly recommend it. It's beautiful, mostly wilderness and there is tons of stuff to do.
I recommend:
1. Deep sea fishing in the Gulf of Alaska for halibut and lingcod- use Pro-Fish-N-Sea out of Seward.
2. A day cruise along the Kenai peninsula fjords to the see the massive glaciers that drop into the ocean.
3. Short 2-3 hour hikes into any number of national and state parks, like Exit Glacier Park.
4. A flightseeing trip to Denali National Park- I used Talkeetna Air Taxi based in, yes, Talkeetna. And pick the glacier landing option. Yes, you get to land on a glacier. And your flight might be delayed due to a moose on the runway.
5. A day long bus tour into Denali National Park to view moose, caribou, bears, wolves and lynx- as well as spectacular mountain scenery.
6. The northern lights in Fairbanks. Amazing! (but impossible to shoot with a mobile phone...)
7. A stay in Girdwood, just south of Anchorage.