@lostinyoureyes
Here are some ideas in no particular order:
Hike diamond head, manoa falls
Take a walking tour of Downtown; hiking books and guide books for Oahu print a suggested route.
Bishop Museum
Arizona Memorial (but I went a couple weeks ago and they were closed due to construction)
Brasserie Du Vin, Meditteraneo, Yama’s Fish Market, Side St Inn, Murphy’s, Nico’s @ Pier 38, Jimbo’s (make their own noodles), Haleiwa Eats are a few of my favorites.
Liliha Bakery’s cream puffs and Leonard’s malasadas are local favorites (but are overrated so don’t get too excited).
Hanauma Bay for snorkeling; if you are fit you can do the koko crater hike in the same day – they are right next to each other
Waikiki
Waikiki Aquarium (the Natatorium is right next to it, and is the focus of decades of debate)
Stadium swap meet (W and Sa)
Kapiolani Community College’s Saturday morning farmer’s market
Kailua town has lots of cute shops; Byodo-in Temple, Ulupo Heiau, there are a couple of other attractions along the windward side of the island going in that direction – consult a guide book for all the info.
I won’t divulge my favorite beaches because there are way too many people there already.