We didn't ride bikes on Oahu so can't recommend any trails. Definitely walk to the top of Diamond Head - it's not hard and the view is breathtaking. When you look down on Waikiki and see a tiny pink hotel buried beneath the high-rise hotels, it's hard to believe the Royal Hawaiian Hotel was one of only two hotels on the beach in the early '40s, and was reserved for use during the war years by US Navy personnel on leave !