The local beaches are full of people wearing hawaiian print bathing suits and board shorts. For many great hawaiian print suggestions, check out Hilo Hattie's online store at Hilo Hattie . If you don't have any aloha shirts and don't want to buy any, don't worry just wear normal clothes. If you'll be walking around a lot, tennis shoes or walking shoes are a must. Baseball caps work ok, except they neglect the back of your neck.
Straw hats with a wide brim are better.
Don't worry about looking silly straw hats are very common here, I always wear one when I will be out in the sun. One more thing, wear sunblock always. Buy 30 spf waterproof and sweatproof sunblock and put it on 20 to 30 minutes before going outside and reapply it often. Even if you are just out on a sightseeing tour, you'll be surprised how fast the sun affects you even if it's cloudy out. Nothing can ruin a vacation faster than a nasty burn, and in Hawaii, it can happen quickly.