Fairbanks is no longer the backwoods hole in the wall it once was. There are now several 'name brand' hotels to choose from. On the high end, there is Princess Lodge, Pike's Landing, Sophie Station and Westmark. Those are the main hotels the cruise lines use to put their passengers in. Away from the airport (but not too far in our neck of the woods) is Springhill Suites, Hampton Inn, Holiday Inn Express, Best Western and Alpine Lodge are all decent places around town. Then on the lower end, is Comfort Inn, and Super 8. For three nights, I would recommend Hampton Inn, Holiday Inn Express or Best western. All are fairly new and offer their own brand of amenities.
I live just down the road from Fairbanks and will be happy to answer any other questions you have.
Just an FYI Stayed in Sophie Station when we did our landtour and a great hotel but away from the city proper. Will have to take the shuttle or if you rent a car you will be fine. The hotel itself was great. Susan