I dived in Kaneohe Bay and outside it for a number of years. Once you come off the coral heads, the slopes just drop off to 55'-60'. It's surreal down there - you swim through clouds of sediment and then there's 18" of clearish water above the moonscape bottom. The bottom has big holes - some 4" across that I always thought were mantis shrimp burrows. There are a lot of them in the shallows, so why not the depths? One guy stabbed one that was full 12" long - gorgeous nasty critters that can break the glass in an aquarium.
We went looking for a solid gold Rolex that a Japanese guy dropped - the muck was at least 8' thick before we gave up. The watch is still there...somewhere.
There were huge tigers living offshore - the Shark Task Force dragged in a 16' after someone got eaten, and in the sea caves off Moku Manu, someone claimed to have seen a resident 20'er.
I never saw anything big swimming in the bay itself, but I hit a huge mud cloud one day where something huge coming towards me on the reef slope turned around quickly and left. Interestingly enough, that was my turnaround point as well, and I spent the rest of the day driving the shuttle boat.
I don't know about any shark research center, but there is a UH Marine Biology Center on Coconut Island - the school finally wound up with the whole island instead of sharing it with someone who had an estate there.
During WWII, the base there was a pilot training station and a lot of guys ate it in the bay - off the runways, it's 60' to 75' deep with decades of stuff dumped there - planes included. There must also be miles of scrapped steel cable and riprap so getting entangled in the murk would not be too hard. Someone two feet away wouldn't even know you were in trouble so no one dives there.