Mods, this might best be moved to the Alaska forum.

Basically, you have the 2nd and the 3rd to explore our largest state. Driving to Fairbanks is about 6+ hours (approx 360 miles). I wouldn't try to make a round trip on the same day. Up to Denali and back is doable for a one day outing, however. Leave early (7 AM or so), be at Denali before noon, spend four or so hours touring and looking at wildlife, then back to Anchorage. If you want to pack more in, you can see the old mining town of Talkeetna, or go by Sarah Palin's house in Wasilla.

A second day trip worth experiencing is to go south to the Kenai Peninsula. This takes you around the Turnagain arm of Cook Inlet, past the ski slope at Aleyeska, and you can take the short road to Seward or, alternately, the longer trip all the way to Homer. Either is enjoyable.

Plenty to see and do in the Anchorage area, also.