First, renting a car in Alaska. This was a huge expense. Not only did we want a minivan for 10 days, but we also wanted it to be a oneway rental. You can imagine how not cheap that was. The oneway rental was because our cruise was leaving from Seward, so we wanted to drop the car off there. There are several train or bus options between Anchorage and Seward, but in the end that wasn't practical for us.
There are 2 main things we did to save money on the car. One, I joined AAA for their 15% discount at Hertz. Yes this rental was expensive enough that the money saved more than covered the cost of membership. Two, we didn't rent from the airport in Anchorage (see you knew I had to tie this in to Anchorage eventually). Here's the secret - Hertz has another rental office a mere 10 minutes away from the airport. They close at 5pm, but as long as your plane arrives before then, just hop in a quick cab and go pick up your car there. We saved over $600 from this alone. Not bad for a $20 cab ride.
Here's where we stayed - the Arctic Adventure Hostel. At less then $50 a night for a room for two, this was a great deal compared to other options in Anchorage. True, the bathroom was shared, but I'll tell you I've stayed at a lot of hostels and I had absolutely no complaints about this one. The people who ran it were super friendly, and even offered us some bear spray and fuel for our camp stove that other guests had left behind.