If you want a real local vibe this is the Waianae is the spot. There are really nice beaches close on the West side of the island. If you want to visit North Shore, Kailua (East side), or Honolulu you are looking at about 45-60 min drive.
The airbnb is conveniently located near a lot of really good local restaurants and Tamura supermarket.
Elizabeth's place is exceptionally clean and has just about everything you need. The value for what you get is probably the best on the island.