There are tons of great hikes on Oahu. It depends what you're looking for. Stuart Ball's Oahu hiking book is a good place to start. Dayle Turner does many good write-ups of trails online at a couple of different sites. (google Dayle Turner hike)
Depending where you're coming from, expect Oahu hiking to be hotter, more humid, with worse footing (and occasionally downright dangerous), civilization in view, and stunning scenery. Be careful. Most places present hikes as being scary and they just aren't. In Oahu it's sometimes the opposite. A lot of accidents happen because of steep dropoffs and crumbly or muddy volcanic soil.
My favorite Oahu hikes:
Ka'au Crater (Climbing up a stream past waterfalls, some sections with fixed ropes for aid, technically illegal but no big deal as long as you park legally and enter quietly)
Mariner's Ridge (very short quick climb up to the ridgeline, also technically closed, but EVERYbody uses this trail)
Maunawili Demonstration Trail (winding up down and around some beautiful cliffs)
Kealia and beyond (northwest part of the island)
Kaena Point in winter has seals and albatross.
Any/all of the ridge trails that head upward from Honolulu are beautiful and good workouts. Kuliou'ou is fairly easy and pretty. Hawaii Loa you have to have one person with a Hawaii I.D. to check in. It has maybe the best views. Lanipo is the longest and hardest. Mt. Olympus can be muddy but it's another great one.
Going up Ka'ala, the highest point on the island, isn't easy. It's messy, climby, and can be confusing. But it's a great climb if you have good weather. Lots of people like climbing Olomana, but for me the climbing with the dropoffs at the top isn't fun. I've done it 3 times now, and i always end up saying i'll never do it again.
have a blast...
Oh, and here's a link for the trail system closest to Honolulu. Some real gems in this system, and no losers. http://www.state.hi.us/dlnr/dofaw/nah/H ... System.pdf