You may want to visit Aulani's website(go to activities and look at excursions and daily 'Iwa) to get an idea of all the excursions and daily activities they offer. I was there last July and only did one of the Aulani excursions(Polynesian Cultural Center) because, at the time, most required you to get to Waikiki to pick up the tour. Aulani has since gotten more tour companies to make the drive to Aulani to pick up their guests for certain excursions.
As a PP said, the Paradise Cove Luau is a 10 minute walk from Aulani. The excursions page also lists Germaine's Luau and another one. Check tripadvisor reviews to see which one is best for your family. The Polynesian Cultural Center has a luau but it wasn't included in the Aulani excursion, ambassador dining(prime rib buffet) was. However, some people changed their dining once they got to PCC to the luau. Aulani has the Starlit Lui which has the music but no food. Even if you go to a luau, this is something you should see also--it's free and it's good.
I rented a car at Aulani for three days and did the following things on my own: Pearl Harbor, Bishop Museum, Honolulu Academy of the Arts, 'Iolani Palace, and Diamond Head. I did PCC with Aulani and was glad I did because we were gone for about 12 hours. The Ha, Breath of Life show is great! PCC is an hour away and we made quick stops at the North Shore and Dole Plantation on our way there. I wasn't impressed with Dole and was glad I hadn't put it on my itinerary!
There's a lot to do on Oahu and you won't be able to do it all in one trip. Pick your must haves and plan on coming back.