Yet one more vote for the BI, and the Kona district in particular!
Very laid back, tremendous beaches (especially those only reachable through hiking and/or 4-wheel drive vehicles), the volcano, the observatory, Waipio Valley several impressive historical sites, and the snorkeling . . . rivalled only by a few place in/near Maui.
I suggest renting a decent SUV and going to Makalewena Beach . . . un-freakin'-believable! A very long beach of powdery white sand, and because access is somewhat limited, very few people. We went on a weekday and there were probably a dozen or so other people there, and this is a huge beach!
Sadly, one of the best spots on the whole island is now under limited access due to the recent earthquakes . . . the area near the Captain Cook monument at Kealakekua Bay. Used to be that you could kayak over and spend the day . . . now there's no being on the land. Snorkel tour boats or kayaking without landing are about your only options. Hoping it changes by the time of our next visit, our kayak trip was our most favorite thing of all.
If you want a party atmosphere, sure go to Honolulu . . . if you want a taste of real Hawaii, the Big Island is the choice.
I've been, am going again in October . . . shoot, I even bought into a time-share.
As for airfare, don't forget to check the airlines themselves. Through United's vacation link, their airfare plus rental car blew anything Orbitz or Travellocity had . . . just for airfare.
And if you do any snorking, the fish love frozen peas.
Unfortunately, this is the one thing I would have to advise against, feeding the fish. Sure, one could argue that the fish are already so conditioned to it that it won't make any difference, but it is contrary to what responsible tourism is about . . . the fish quickly learn to rely upon humans as part of their food supply, and it creates very unnatural behavor. Besides, there's so much to see under water that there's no need to artificially attract them, you'll be dodging and mingling with the fish just as if you were one of them.