I'll agree with PIONEER that if you are taking the highway or railroad between Anchorage and Fairbanks you should stop and spend a day or two at Denali.
If you're into hiking and the outdoors, there is some great hiking in the Fairbanks area. Angel Rocks is a good day hike. In addition the University of Alaska Museum of the North is outstanding, and Riverboat Discovery is touristy but worth doing. A drive out to Chena Hot Springs can also be fun when combined with a soak in the springs. You're likely to have better summer weather in Fairbanks than Anchorage, so that may factor in to your plans (especially if they involve being outside).
As for Anchorage, it really depends on what you are in to. Anchorage has more touristy things to do than Fairbanks, but Fairbanks is more "Alaskan". It really depends on what floats your boat.