I have a flight that will get me into FAI at 2 am in February. Rental car offices seem like they are closed at that time. Is there a hotel with a shuttle service at that hour? I need to stay close to the airport so I can pick up a car in the morning.

Also, for those with FAI experience. If I am leaving for BRW at 7:50 AM on Saturday, what is a recommended time to arrive at the airport?