While Fairbanks is good, Denali is arguably better.
Alaska in general, from its Arctic vantage point, offers exceptional views of the aurora borealis. It's well within the Northern Lights zone, and its winters offer nearly constant darkness morning to night. Fall, too, offers excellent views [source: Mother Nature Network]. If you're lucky, you can see the lights even outside the prime viewing seasons.
Denali National Park, a bit south of the Arctic Circle and just a few hours from Fairbanks, offers millions of pristine acres where city lights won't compete with the ones in the sky [source: Explore Fairbanks]. There's lodging there, too, so even the less-outdoorsy types can venture comfortably into the Alaskan wilderness to catch the show.
Next, a bit eastward ...