As far as I know, late August and early April are the suitable time to view the
northern lights of Alaska. My friend has gone to Fairbanks last september and he said he saw the aurora borealis or northern lights on Sep.22nd on a new moon night. He went outside town, away from the city lights and found it very late night, he said that it was really an unforgettable experience.This Northern Lights can't be seen through out the year, only few days are possible.
This may help you decide to make your Fairbanks trip to see the Northern Lights! best of luck!