I'm an owner at Morritts! If you've never been there it's a haul from Georgetown- a good 45 min or so. We dive with Don Fosters in Georgetown, but I've heard good things about Ocean Frontiers
Scuba Diving Adventures & Dive Vacations - East End, Grand Cayman, Cayman Islands - Ocean Frontiers Home Page which is way closer to Morritts. I would stay away from tortuga divers, which is Morritt's dive op- they are very pricey.
Have fun! Is this your first time??