Thank you to everyone for your help and suggestions. We based our time in Oahu on the filming sites from "Lost" and we had an amazing time. Our "Lost" focus really helped us to see the entire island and places we never would have otherwise found. And of course, we did some other fun things too.
Day 1--arrived, checked in at Turtle Bay Resort. Ate dinner at Ola on the beach.
Day 2--Ted's Bakery for breakfast, Waimea Falls (to see Kate & Sawyer's waterfall), Mokule'ia Beach (plane crash site), YMCA Camp Erdman (the Others' Village) which was completely surreal, Police Beach (survivors' beach camp), Waialua Sugar Mill (Mr. Eko's Nigerian village), and then cleaned up and went to Nobu in Waikiki for dinner and dessert at Liliha Bakery (the "diner" where Kate met her mom)
Day 3--2 hour ATV tour at Kualoa Ranch which was without a doubt, one of the best parts of the vacation. Saw amazing sites, "Lost" and otherwise, and drove through the set of the Journey to the Center of the Earth sequel which is filming there. It was raining but that only added to the fun. Also did the ocean voyager tour there which was cool too. Then had shave ice at Aoki's in Haleiwa and headed back to Turtle Bay for dinner at 21 Degrees North.
Day 4--spent the day at Turtle Bay and tried to see the famous Banyan Tree but they were filming Journey 2 there as well (!) so we were blocked. Went to Alan Wong's for dinner and had the vegetarian tasting menu which was delicious.
Day 5--breakfast from Ted's, Byodo-In Temple (where Sun & Jin got engaged), hiking at Makapuu Point (Other's camp), Hurley's mom's lottery house, brunch at Orchids, "Desmond & Penny" pics at Ala Wai Yacht Harbor, then Diamondhead.
Day 6--finally saw the Banyan Tree at Turtle Bay, snorkeled, had lunch at Haleiwa Eats and shave ice at Matsumoto's, stopped and saw sea turtles on the beach, went into Honolulu to see the convention center ("Sydney Airport") and Ala Wai Canal where Jin and Sun first met, then off to the airport and headed home.
I think that's it--we had a phenomenal time, despite rain for the first 3 or 4 days, and are looking forward to coming back someday. Thanks again for the tips and recommendations! :)