I'd have to say:
#1 - Whatever you do, GET OUT OF THE CITY. Waikiki is great, but you can see cool cities anywhere.....it's the rest of the island that is a unique experience!
#2 - Get in the water with some critters. First timer or nervous? Go to Hana'uma Bay. More adventurous? Go to nearly ANY protected bay or cove (Shark's Cove near Waimea is a great locale for a less-crowded explore).
#3 - If you have kids with you, focus on the truly memorable (i.e. skip the zoo, water park, shopping, etc.) - the Polynesian Cultural Center, the Dole Plantation, Hana'uma Bay, etc. My clearest two memories of my first visit to the islands as a kid are (1) climbing around in huge banyan trees and (2) seeing active lava in person.
#4 - If you enjoy shopping, but aren't looking for the mall and designer stores (i.e. you prefer the International Marketplace), be sure to visit the regular "flea market" at the Aloha Stadium - great deals, great selection of lower-cost items, great people-watching, and even better conversations....
#5 - Visit the wild and feel the spirit of the islands. It doesn't matter if you're in the rainforest on Tantalus Drive, in the pass at Nua Pali, the dry scrub of the leeward coasts, or the barren moonscape of the lava fields - THIS is what the islands are. If you spend your whole visit in the city, on the beach, and in the tourist attractions, you really owe it to yourself to take an afternoon to visit one of the botanical gardens or go for a hike. The mana of Hawai'i will return your appreciation.