I would stay the whole week at Aulani rather than split stay. I don't feel Oahu is big enough to warrant a split stay. Aulani is within 30-45 of most major tourist destinations as long as you plan around rush hours or weekends on the North Shore. I am not a city person on vacation, so Waikiki was not my cup of tea. Since we've visited Oahu on multiple trips, we generally skip Waikiki. Waikiki feels like visiting Southern California beach cities or Miami with the traffic, typical chain stores and restaurants, police sirens, and loud rap music. I was satisfied visiting Waikiki for a few hours to eat dinner, see the Royal Hawaiian Hotel and the main beach, and visit some unique shops. Since I love Disney Resorts, I know I would be let down staying in Waikiki unless maybe at the beginning of the trip if you don't have enough points for your entire stay at Aulani.
I would rent a car rather than rely on Rideshare. I've spent between $200 (2023 trip) and $800 (2021 trip) per week in mid-August.
I love visiting Pearl Harbor as a proud grandchild of WWII Veterans. I see one PH museum per trip; visiting all the PH museums may be overkill.
Food: I love Japanese food in Oahu, such as Marugame Udon in Waikiki, Kazoku, Tanaka Ramen, Curry House Ichibanya in Kapolei, and Kikuya in Honolulu.
I also liked the Mexican restaurant Mekiko, which is across the street from Aulani. It was reasonably priced compared to other restaurants around Ko Olina.