Give Giles at Wall to Wall a call or check out his website:
Wall to Wall Diving - Personally Guided Diving at its Best in Grand Cayman
He offers personalized service and doesn't cater to the cruise ships. Since you will be there for several days, you will have quite a bit of say on the dive sites. He set up a night dive just for us and he offers the Cayman Rover which will give you a three tank dive to the East End if the weather is good enough to get around the island.
I was very impressed and pleased with the experience. I wrote a review further down in the forum.
Wall to Wall and Off the Wall are both headquartered in the Lobster Pot Dive Center:
The Lobster Pot Dive Center