Agree that Little Cayman is the place to be. Grand Cayman has more "night life" but pretty commercialized and to me the diving is only so-so. Also agree that Little Cayman Beach Resort is great. Individual bungalows, right on the beach, with nice hammocks and places to walk and ride on bikes. Nice central "restaurant" where you can get meals, or can cook in your bungalow. Bike travel is the way to go around the island.
All depends on what your wife likes to do if she wants a nice getaway where she can read and enjoy peace and quiet, then Little Cayman is the place to be. If she wants tons of other people around, constant high dollar shopping, casinos, and big night life, you’ll want to do Grand Cayman. But if you do Grand Cayman, you’ll miss the really good diving on Little on Bloody Bay Wall. Been both places, and Grand pales by comparison dive-wise to Little. What you really need to do is to get your wife diving, so she’ll enjoy the same things you do....