Another option for travel connections to HI at least from NY is stopping in Phoenix. Whenever I have looked at least from NY for good connections,San Diego never comes up as an option although San Diego and Coronado, my particular favorite place to stay is a great place to visit. Travel really depends on when you are going and what airline schedules work the best.
Personally I prefer the big island as the most interesting . Haven’t been lucky enough to get to Kauai though. Wherever you go I recommend buying the Kona coffee to take back with you in either local supermarket or in Costco, in Maui It is however interesting to visit one of the coffee farms on the big island. I found that the big island has more scenic waterfalls and spots to stop and see views than the road to Hana. When we did the road to Hana, the road was in serious disrepair and along that road you are following sometimes soda delivery trucks, construction vehicles, school buses, and there are only a few places to safely pull over to stop with many No Trespassing signs on property along the road. With one-way bridges sometimes you needed to back up to allow oncoming traffic to pass and that was not fun. Hana itself not especially interesting in my opinion although I have been told you need to stay there and either travel past Hana or go to sites around Hana. Actually before you begin driving the Hana road there is beach area that is very scenic with big waves and we got to watch many surfers there.
Costco is conveniently located on the way to airport in Maui by the way so that you can fill up your car but it is very crowded so you need time to do so and only place in which we have been approached by people with cans asking if we can pay for their gas.