Flight
As an alternative - for anyone who wants to see southern Alaska (highly recommend in the summer) and is renting a car through a major chain - you can fly into Fairbanks and fly out of Anchorage or vice versa. The drive is beautiful and it lets you go down to check out the Kenai Peninsula.
House Or Rental
AirBnB will likely be your cheapest option, but be aware you will need to book early! A large portion of cabins up here are "dry" - that means no running water. These will have 5 gal+ jugs and a grey water systems for basic water needs and outhouses for bathroom needs. There are many locations in town where you can get a shower if you opt to get a dry cabin, including B&C Laundromat (my personal favorite for their massive dinosaur collection on display and sometimes dog buddy).
Travel Note
907-347-2438 My favorite cabby - top pick if you want the full wacky-Fairbanks experience.