French Polynesia is also along that route. I took the ANZ flight from LAX to Tahiti which ultimately continued to Auckland. I seem to recall that flight or another connection available had a stop in RAR.
Once in Tahiti you have several options in the local area - most people would tell you not to stay on Tahiti but to go to one of the other islands like Bora Bora or Tahaa. Other options that you can take a short flight to from Tahiti are islands like the Marquesas and Moorea (Have not visited those myself)
Depends on what you are looking for and what your budget is, we did an incredible two week trip where we spent one week on a boat going around the islands near Bora Bora and then spent a week on Tahaa. It was a huge splurge, but it was really nice. The boat was particularly expensive, but it was also surprisingly empty so maybe you can get a better deal than we did
Travel Agent We Used
Hotel on Tahaa