While Fairbanks is small, it is really spread out. There is a city bus system. You can check out the map and schedule at http://www.co.fairbanks.ak.us/busroutes/
We always recommend people rent a car, if at all possible. The flexibility and freedom allow you to navigate the city on your time and pace. Below are some of the national and local car rental options.
Alamo 1-800-327-9633
(907) 451-0457
Budget 1-800-527-0700
www.budgetalaskaonline.com (907) 474-0855
Dollar 1-800-800-4000
www.dollar.com (907) 451-4360
Hertz 1-800-654-3131
www.hertz.com (907) 452-4444
Payless 1-800-PAYLESS
www.PaylessCarRental.com (907) 479-0177
Arctic Rent-A-Car 479-8044
arcticrentacar.com/
Aurora Rentals (907) 459-7033
National 1-800-CAR-RENT
(907) 451-7368
RentAWreck
rentawreck.com/cheap-car-rental-fairbanks-AK.html
(907) 452-1606
U-Save 1-800-272-8728
www.usave.com (907) 479-7060