Hawaii is very informal. Shorts, T-shirts, and tennis shoes will get you by at most restaurants and attractions; a casual dress or a polo shirt and khakis are fine even in the most expensive places. Dinner jackets for men are required only in some of the fine-dining rooms of a very few ultraexclusive resorts, such as the Halekulani on Oahu, the Big Island's Mauna Kea Beach Hotel, and the Lodge at Koele on Lanai -- and they'll cordially provide you with a jacket if you don't bring your own. Aloha wear is acceptable everywhere, so you may want to plan on buying an aloha shirt or a muumuu (a Hawaiian-style dress) while you're in the islands.
So bring T-shirts, shorts, long pants, a couple of bathing suits, a long-sleeve cover-up (to throw on at the beach when you've had enough sun for the day), tennis shoes, rubber water shoes or flip-flops, and hiking boots and good socks, if you plan on hiking.
The tropical sun poses the greatest threat to anyone who ventures into the great outdoors, so be sure to bring sun protection: a good pair of sunglasses, strong sunscreen, a light hat, and a canteen or water bottle if you'll be hiking -- you'll easily dehydrate in the tropical heat, so figure on carrying 2 liters of water per day on any hike. Campers should bring water-purification tablets or devices.
One last thing: It really can get cold in Hawaii. If you plan to see the sunrise from the top of Maui's Haleakala Crater, venture into the Big Island's Hawaii Volcanoes National Park, or spend time in Kokee State Park on Kauai, bring a warm jacket; 40°F (4°C) upcountry temperatures, even in summer when it's 80°F (27°C) at the beach, are not uncommon. It's always a good idea to bring at least a windbreaker, a sweater, or a light jacket. And be sure to toss some rain gear into your suitcase if you'll be in Hawaii between November and March.