We priced it, and I want to say that a full size with all the fees tacked on to the rental rate for our time period was about $100 a day at Aulani and the smaller car was not that much cheaper at that time. Without a car, you also have to figure out transportation to and from the airport, which is 20 miles from Aulani. If you rent something smaller than a "full size" car, the cost for a taxi or shuttle to and from the airport alone can be as much as, or more than, renting a car for a week. When we were checking options, the Disney parking was the only thing that made a week long rental cost us more than airport transfers and a one day rental--- we decided we would prefer to pay the parking to have the freedom to come and go as we chose on our time schedule. Also, when we were driving our rental car, we were free to stop along the way at anything that caught our interest. We were not locked into straight travel from point A to point B. We could stop wherever we wanted for as long as we wanted and then more on to the next place. We were glad we rented a car, even though when we were there, we ultimately made the decision to spend more time at Aulani than originally planned. I will say though that if you are ONLY going to Oahu and ONLY staying at Aulani, it is a good idea to branch out and see some other places- we did that later in Maui, so we decided to focus on Aulani. When we got home, DH dubbed Aulani "fake Hawaii"- which is not to say that he doesn't absolutely love it there, because he does and he thinks it is amazing. It is just "disneyfied" Hawaii-- everything is Disney created- right down to the Lagoon- to be as perfect as possible. To see "real" Hawaii, you have to leave the wonderful Disney version and explore. We were very happy in the Disneyfied version and wanted to spend as much time there as possible!
We got a full size rental car for the whole 6 days of our trip using a one week rental including all tacked on fees for right around $300 (and I've seen people get it around $200 at different times and we could have gotten it significantly cheaper if we picked a smaller car). I just looked at the uber estimator and it estimates from the airport to Aulani is between $80 and $113 (I think they have had some issues with the City resulting in restrictions and regulations on picking up people at the airport), which I think is about the same as a cab or shuttle. So if you factor in the cost by taxi to and from the airport (and it doesn't look that different from UBER at least going from the airport- might be cheaper returning to the airport), all we would have saved by having a car for one day instead of our whole trip is the Aulani parking fees. For us, it was worth that to have the freedom to go where we wanted whenever we wanted.
I see OP mentioned the Polynesian Cultural Center-- I was worried it might be a little too cheesy based on some of the reviews, but we enjoyed it. DD (10) absolutely loved it. We did the luau with the ambassador package, and although normally I am a tour on your own without a guide, type person, we loved having the guide and learned a ton about the Polynesian culture.