Pick up a copy of the Milepost, it is well worth the money. It will give you information about what to see, where to stay etc.. Lived in Soldotna for a couple of years so here are some of my favorites.
I would recommend Denali, stop in Talkeetna on your way to Fairbanks. The river boat cruise in Fairbanks was o.k, very touristy.
Head south of Anchorage on the Seward highway one of the most scenic in North America. Sometimes you can see beluga whales along Turnagain Arm..lots of picture opportunities.
Check out the Exit Glacier in Seward and the Sea Life Center. Head back towards Cooper Landing and watch them combat fish for salmon along the Russian river. When you get to Soldotna/Kenai, you must stop at Sal's for their big cinnamon roll. Drive down to Homer and view the volcano's Iliama and Redoubt along the highway. Homer is great for halibut fishing, lots of good charters to take out of either Homer or Seward. Homer is the home port for the Time Bandit from the Deadliest Catch. Walk along Homer Spit and stop at the Salty Dog for a brew and be sure to leave your business card on the wall.
Whatever you decide to do, you'll have a great time. Drop me a line if you need anymore info.