Based on your listed priorities:
1. Beaches - Kauai has a lot of very nice beaches (will require some driving) without lots of crowds. In fact, this is the island to go to if you want to find a secluded beach for just you and your SO. Also, you could literally go to a different beach every day of your trip while on Kauai and not have to repeat any.
The Big Island also has some nice beaches, maybe not quite as many or quite as secluded. Though it is definitely worth visiting the black sand beach there.
The man-made lagoons around the JW on Oahu are nice, but as mentioned earlier, they just feel "man-made" at least they did to us. But if you like to people watch while at the beach or like to be around lots of people, then Oahu is where you can get that. Waikiki beach may be a great place to visit for you. Of course the JW is a bit of a drive, but the JW is also probably the nicest of the "hotels".
2. Good Food: Oahu will have the best and most varity of food choices. Though most of the good restaurant options will be a bit of a drive from the JW. Both Kauai and the Big Island will have fewer options. Though both do have some nice places to eat. And of the two, Kauai probably has more options than the Big Island.
3. Adventure Activities: Kauai being the oldest, having the only navagatable river, and having the largest canyon (Waimea is the 2nd largest in the US) on any of the islands has a number of options that the other two don't have. It also has more waterfalls and water holes to swim in. A helocopter ride is truly an experience here. There are day hiking/kyaking/hay riding tours that even include jumpting off a waterfall should you be brave enough.
Kauai isn't called the Garden island and the most "Hawaiian" of the islands for nothing. Also, most any "deepest darkest jungle of Africa" or prehistoric jungle movie was actually filmed on Kauai. A lot of the tours will show you where the prehistoric tree with the weird roots from
Jurassic Park is, where the initial scene from
Raiders of the Lost Ark was filmed, or a number of other movies.
The Big Island has something you may never be able to see anywhere else in the world: A volcano up close and personal. There are day tours covering a good portion of this island that are excellent and heliocopter tours here are awesome as well. Also, the Black beach mentioned above is worth visiting just to see it.
Pearl Harbor is probably the biggest draw to Oahu and well worth visiting. There is also the Polynesian Culteral Center and the Dole plantation with its hugh garden maze. If you drive up and down the east side of the island you can see some great ocean cliffs and parks. We found a real reasonable daily rate to charter a fishing boat from Oahu. It was great (except my wife got sick while out at sea). You can definitely find fishing tours from any of the islands, but when I last checked, we found the best charter boat prices from here.
One more point: Get some good Hawaiian Tour books. The best one we found for Kauai was "The Ultimate Kauai Guidebook - Kauai Revealed". By far, they had the best advice and really laid out what to do on Kauai. I think they have "Revealed" books for the other islands as well.