Welcome to Alaska.
If it were Anchorage you could head over to my place or The Peanut Farm is the place to go as it has a plethora of TVs to play any channel of your choice. Not sure what the Sports Bar scene is in Fairbanks but assume most hotels should have FOX available. I do see that the Clarion Hotel (95 10th Avenue) has TVs in their "Tubby's BBQ and Sports Bar" and they get pretty good reviews for their wings and other menu items. Would call ahead though to make sure they will broadcast your channel of choice. Their number is (907) 457-8899.