I think the plane wreck is the Corsair, but I can't get a close enough look at Catherine's avatar to be positive. I'm notoriously bad on identifying the different wrecks. Anyway, if it's the Corsair, it's off the east shore of Oahu.
Staying at the Waikoloa you have a couple of options. You can choose to drive closer into town to meet any of the operators there, or you can go with Red Sail, which is based right out of the resort. The drive into town averages about 30 minutes, depending on when you go and traffic conditions. If you don't mind the drive, there are tons of recommendations here for dive operators based out of town.
Red Sail is right in the resort. I was up at the Waikoloa last August for a 3 day weekend. Because I was only staying for such a short time, I didn't want to spend a lot of time driving into town. I did a couple dives with Red Sail and had a really good time. Both dives were shallow, and perhaps you can inquire if your wife can go along as a snorkeler.
If you want to do the manta dive, you'll have to drive down to the harbor close to town. Although your wife doesn't dive, she can snorkel the manta dive if she wants.
The resort itself is huge and has several pools with slides, a lagoon type area with fish and turtles that you can rent paddleboats, kayaks or snorkel gear from. Nice spa and typical resort shops. King's Shops are nearby and there's a shuttle that can take you there for a dollar or so. If your wife prefers not to go with you on the dives, there's enough at the resort to occupy some time.