Excellent ideas here. I would suggest you stay as long as possible. We've been to Oahu 3-4x? Maui 2-3x, Kauai 3x and Big Island 2x now. (Ok, seeing that written out, I guess I am a HI addict) With kids, we stop over in LAX on each way from NYC. We fly AA, and there are early AM flights to HI that leave LAX that get you to HI in the early afternoon. With kids, for example, we will take a Saturday AM flight from NYC, get to LAX by noon, have lunch, stay at an airport hotel with free shuttle (the Sheraton is the best), and have some pool and hangout time and then early to bed. Early flight out of LAX on Sunday AM, arrive in HI early afternoon on Sunday with a head start on the jet lag already. On the way home, it's usually harder to stop over in LAX because the flights out of the islands are either early AM or late afternoon (or only late afternoon). When we were on the Big Island in January, our 4pm flight got continually delayed and we landed at LAX at 1AM (with 2 kids), then transferred to the Sheraton for a 4 hour nap and then an early flight back arriving in NYC late afternoon.
Since you're 2 adults no kids, I'd say on the return, it's probably worth it to take a redeye back to the East Coast, then you have a full day in HI before you leave. When we traveled to HI before kids, we would layover in LA and overnight (you don't really lose much time, and save 1 night's hotel in HI!) on the way there, but take a redeye on the way back. Keep in mind that you'll most likely be renting a car when you arrive and may drive significant time to get to your resort, so it helps to be somewhat fresh on your way in. Less so on the way back.
If you go for at least a week, I would suggest AT MOST 2 islands, preferably 1. And agree with PPs that you do not want to fly all that way only to spend it at your resort. IF you decide to use DVC points at Aulani, I might do 1-2 nights at the beginning if SW only flies to HNL, and then spend the rest of the time on another island. The Big Island is my favorite, but it's REALLY big. We have been 2x, once for a week with little kids, and once for 4-5 days without kids, and feel like we've only barely scratched the surface. I also really love Kauai because it feels so relaxed. Oahu and Maui are the most touristy and have the most people, so we've gone there less on recent trips and tend to spend time on Kauai and the Big Island. The Big Island is so big that when we went without kids, we flew into Hilo, stayed a few nights at the volcano, and then went to Kona for a few nights and flew out from there. And still missed everything in between.