CO has the only nonstop from NYC and it is just to HNL, so you would still have to take an intra-island flight to get to OGG and KOA. On all other airlines, you'll have to stop at least once even going to HNL.

I took AA last fall and it was a very good experience. Do a search on aa.com and you should be able to find first class fares for around $1250 each. If you choose AA, then it's best to not go through LAX because most of the AA flights are on 757's now which have awful first class seats. Instead, fly to ORD or DFW and then go from there to either HNL or OGG directly. This is also a good idea on the way home because you will get one long flight on which you can try to sleep rather than having to stop in CA halfway back. AA has flights from KOA to LAX, but again these are on 757s with poor first class seating.