Obviously, you're getting a lot of different ideas and recommendations. Everyone has their favorite place. This is my wife's and mine.
We've made seven dive trips to Grand Cayman ... stayed on Seven Mile Beach, Sunset House and Cobalt Coast ... dove with four different operators. Our last four trips have been to Cobalt Coast and Divetech. And, we'll be going back again, next year.
We have many reasons for why we keep going back to the same place. Starting with the diving. Cobalt Coast is located on the northwestern shore of Grand Cayman. Whenever the winds are favorable, you'll be diving the north wall. That's not something you'll be able to do if you're at Sunset House or diving with one of the SMB operators. Like others have said, the north wall offers great diving. The wall and reef architecture at sights like Ghost Mountain and Princess Penny's Pinnacle is amazing. It's also a great place to spot Eagle Rays and larger fish.
When the winds aren't favorable for the north wall, you'll dive the west wall. But, you'll be at the northern sites away from the cruise ship crowds and the Georgetown mob.
The Divetech crew are great DMs and instructors. Divetech is well known for its kids' programs and for being expert trainers in tech diving and rebreathers. One of their instructors was named "instructor of the year" this year by Grand Cayman's dive operators association. I can say from experience, that all of the Divetech instructors are very good teachers. Even though your wife is only doing her check dives, I think she will appreciate their attention and profesionalism. She won't just get her ticket punched.
There are always three DMs/Instructors on each dive boat; two in the water and another topside with the boat. They do a great job of combining vigilance with humor. They'll give you as much independence you want, but they'll also keep a very close eye on you while they access your diving skills and if they see a problem, they'll be quick to deal with it. That said, they give the most complete and most humorous dive briefings I've attended anywhere. Over the years, and many dives, they have become good friends.
Cobalt and Divetech offer the best shore diving anywhere on the island. Actually, there are two sites; one at Cobalt Coast, the other at Lighthouse Point, about a mile or so down the road. This is also good because if it's too windy at Cobalt, LHP is nearly always wind free. If you're diving with them, Divetech is great about taking you to and from LHP. Both reefs are very healthy and offer a lot to see in both varieties of coral and critters. My favorite night dives have been off Cobalt Coast where I've typically seen octopi, eels, lobster, porcupine fish, squid, etc.
Cobalt Coast is also very unique. It's more like staying at a bed and breakfast than a hotel. From the moment you arrive and the owner, Arie, greets you and takes your bags as you step off the van you'll experience a level of service that you'll find in very other resorts around the world. It's as impeccable as it is casual. Your treated like a friend; not as "the people in room 443."
The suites are spacious and clean. You'll like the big, european style tub and shower.
And then there's the restaurant. If you want to party, Sunset House is the place to go. But, if you want good food and a good deal, then Cobalt Coast can't be beat. My wife and I have been to all-inclusive dive resorts elsewhere in the Caribbean. While the diving was great, the food was pretty mediocre. Not at Cobalt Coast. The menu has an excellent mix of salads, appetisers, sandwiches and entrees. The nightly specials are excellent and the soup of the day is always to die for. If you like food, you'll enjoy Cobalt Coast nearly as much as the diving.
I could go on and on. I'll just say that while every resort and dive op claims to have the best diving or the best rooms and accomodations, you won't find any with the same warmth, service and friendliness as Cobalt Coast and Divetech. And, when you come here, you'll be meeting old friends for the first time.