Before we moved up here, I'd come for my vacation each year to spend time in our cabin and car rental was a HUGE expense.
One year the Wife and I wanted to drive the Denali Highway. The major rental companies would not allow their cars off the pavement, so we found a used car lot that rented their stock. It was a lot cheaper. The car was not new, but it ran fine. I don't remember how we found that lot (not a new dealer lot), but there must be some more out there (lots of used car lots in ANC). One of the big things about that is you get away from the airport tax!
You can take public transit away from the airport to a rental place and save some $.
There is a system for renting private cars, but I don't know what it's called or how to access it. One year a coworker's family lived up here and offered to rent me his van for about 1/3 the normal cost after he'd heard how much it would cost to rent from a company. It wasn't new but ran OK. They were short on $ so it worked out great for both of us. He parked it at the airport for my arrival and I parked it there when I left. I think he sent me a key before I came and I just locked the key inside when I dropped it off. He even had a couple of bottles of water in there for me. I left a "little extra" as it was certainly a good deal for me.