Check out Kaimana and Hawaiian Diving Adventures. If you're staying on the North Shore, though, somewhere like Deep Ecology may be a better bet.
Note that there's a tug in 65' near Pearl Harbor if you're looking for an interesting wreck within your depth requirements. Kaimana visits it with some regularity, while HDA usually has a fuel surcharge to get there because they're leaving from a harbor closer to Waikiki. Most of the other recreational wrecks are between 80' and 120' (YO, Sea Tiger, Corsair, Mahi, various LCUs).
If wrecks aren't your thing, there are a number of interesting shallow reef sites but I strongly suggest a shore dive or several on the North Shore. If you're up for some walking and whatnot, renting gear and shore diving Hanauma Bay outside the rocks is a great way to see hard coral that's about on par with some of the spectacular stuff off the Big Island. Spitting Caves/Sea Cave around the point between Hawaii Kai and Hanauma Bay are also good sites, but are considered challenging drift dives by local operators because of currents/surf, so it's common to try for them but instead wind up diving a boring 40' sand pit of a reef nearby instead.
To the extent possible, I'd avoid most of the shallow reefs outside Waikiki and Hawaii Kai - they're pretty poor examples of what's alive under the water around Oahu. Unless all you want are giant sea turtles...then, right off Waikiki is where you want to be.