It really depends on what kind of time you have. There is really only a very small portion of Alaska that is even really travel enabled, the highway running basically between three cities (Anchorage, Fairbanks, and Delta). If you have the time I recommend driving the entire highway. You will hit lots of off-road hiking and sight-seeing opportunities (glaciers, animals, Mt. McKinley, etc.) as well as hit many of the more touristy areas. There are really wonderful biking tours available which would be excellent. Obviously this is the summer. The warmest months are June and July, skimming the end of May and the beginning of August. Renting your own car and driving the Alaska Highway really is the way to go. If you are really in for adventure, bring your bike and camping supplies :)