I went to Hawaii on business months ago, and have decided to turn some scraps of paper into a post so that I can remember what my local colleagues recommended. Each one of these little trips would be the better part of a day, and assumes that you are starting in ending in Honolulu. Business trips will tend to place you in Honolulu, but if you are on vacation research the other islands.
1) Beautiful sunsets or just nice scenery. Take H1 until you come to a dead end in approx one hour. Kaena Point.
2) North Shore: shaved ice, shrimp trucks. H1 to H2 past Dole plantation to Haleiwa, consider following coast back to Honolulu.
3) H1 to Hawaii Kai, continue to Makapuu, continue to Waimanalo Beach & Kailua. Return via H3, Pali, or "Likelike Highway (Rt 63).
Also, stumbled upon this hike on TV. Sounds tough, but worth trying once. Koko Head.
My colleague recommended Hau Tree. Seems to get mixed reviews, but she liked it.