I have no knowledge of the AirBnBs in Oahu, but Kailua was one of my favorite areas we visited all trip. It was the most beautiful beach we saw in a quaint town on the windward side of the island, which had a different vibe than the leeward side where Aulani is.
I also think Turtle Bay is a great recommendation and we loved the North Shore. One thing I'll caution is that outside of Aulani and Waikiki, we found the waters to be pretty rough almost everywhere we went . Even different islands. North Shore was among the worst. We were there mid-September, and its my understanding that the winter months draw in rough waters so perhaps we were at the start of that. But I'm not a strong swimmer and there were some instances when I wouldn't go in the water because of this. But with Aulani being on a man-made lagoon, it intentionally breaks the waves and calms the water there making it much easier to swim. There is a big drop-off, however.
We also liked the Waikiki area, but we agreed it reminded us of Miami Beach or really any other major city if you plopped it on an ocean. Beautiful views, great dining and shopping, but much more urban feeling and less nature-y than anywhere else we visited. We still enjoyed it for a couple days though.