I will try to help! We will be taking our 8th trip to the Caymans in fall spending a week on Grand Cayman and a week on Little Cayman.
A lot depends on your budget, the time of year you want to travel, and the non-diving interests of your family and non-diving wife.
In general, I suggest staying away from Georgetown because it gets so crowded especially when the cruise ships come into port. An exception to this would be Sunset House. It is south of Georgetown and they don't have much of a beach but they do have a house reef for shore diving and an onsite dive op. I believe that breakfast is included but you would have to eat out twice a day and that can get expensive. I have never stayed there but we have visited Cathy Church's Photo Shop and Gallery onsite and if you are photographers you will enjoy visiting.
Whatever part of the island you pick, I recommend an apartment or condo. You'll get more space and you can make simple meals twice a day and go out for a nice restaurant meal once per day (or order a pizza) and that keeps down costs and saves vacation time. Mixing some of your own drinks also saves a lot of money. Also having an ensuite washer and dryer (or access to an onsite coin-op laundry) means that you don't have to pack as many clothes.
No matter where you stay I also recommend getting a rental car. Rental car prices are pretty cheap and there's a lot to see and do on GC, it makes it easy to get to and from the airport or to do grocery runs, and you will have the freedom to explore the island. But you will have to be willing to drive on the left side of the road.
I recommend bringing a GPS with you, we use an old Garmin GPS and car charger and it helps a lot - especially when navigating the roundabouts or negotiating the narrow, angled, one-way streets of Georgetown. Some people download Google Maps before they arrive on the island and have had luck using them for navigation but I haven't tried that. You don't want to burn up cellular data or accrue roaming charges.
Seven Mile Beach is very popular and very pricey and if your non-diving spouse loves beautiful white sand beaches and gorgeous turquoise water (and who doesn't?) then it is the best choice - but it can be very expensive, especially during the high season; and the hotel beaches can get crowded during the busy season.
We stayed at the Comfort Suites on 7MB on one of our early trips to GC and it was okay but we didn't go back. The beach was small and crowded but the rooms are suites and offer some meal prep and extra sleeping area for your son so that might work.
If you can afford it, some of the condo complexes on 7MB are very nice and the beaches are not crowded and they offer daily maid service. Places like the Caribbean Club, Discovery Point, and Christopher Columbus - I've never stayed there, I've just heard good things.
They've just opened a new Margaritaville Resort in West Bay and they might be offering special prices to launch the new facility. I don't think that they are on the beach but have beach access, but I am not sure. It might be worth checking out.
Sunshine Suites is a very popular choice. It is across the street from 7MB but you will have access to the amenities of the Westin Hotel and their beach area. They offer both suites and apartments and are considered a more economical option than some of the properties directly on 7MB.
Keep in mind that many of the 7MB hotels and resorts charge a daily resort fee per person, and that adds to the overall costs.
Some folks that want to stay near (but not on) 7MB go north in West Bay to areas near Macabuca. There are several condos in that area but most are on ironshore not beach - but offer good snorkeling.
Staying at a resort that offers an onsite dive op is ideal but most of them are away from 7MB and may not be as attractive to the non-diver, they include Sunset House (already mentioned), the Wyndham Reef on the East End, and Lighthouse Point (and Holiday Inn), and Cobalt Coast on the north end of West Bay above 7MB.
With the exception of Sunset House (which I've heard mostly dives the west side which isn't the best IMO) they are all pretty remote and require some driving to get to restaurants or grocery stores. Cobalt Coast is offering some good specials (see the link below) but it is a no frills kind of place and quite remote from other attractions, see the link below:
Dive Packages
There are some very nice properties on the East End and North Side like Morritt's, Wyndam Reef, The Retreat, and Cayman Kai, but they can be pricey and they are far away from most everything. Plan on a 45 to 60 min drive one-way to the most popular attractions, restaurants, larger grocery stores, and shopping.
We like to stay in the middle of the island with easy access to most areas. We stay at the Turtle Nest Inn in Bodden Town and if you want a condo they also manage the TNI Condos next door. Bodden Town is a more residential and suburban area. It is not near the big attractions but it isn't that far away either. It's about 10 to 12 miles from Georgetown and the 7MB so you will have to drive but a rental car comes with the reservation. It is a small, family-owned operation, not luxurious but clean and nice and well-maintained, and the staff are lovely.
We stay in a one-bedroom apartment at TNI with a full kitchen and I think that the sofa is a sleeper. I recommend beachfront or oceanfront because you may hear noise from the street if you stay in an oceanview apartment. We get daily maid service (except Sunday) and access to a coin-op laundry. If you stay in the TNI condos next door I believe you will have more room and an ensuite washer and dryer (and a dishwasher?) but not daily maid service.
Another thing that we like about TNI is that is has a nice, quiet little beach (not the 7MB but quite lovely) and good snorkeling right out front. The entrance can be a little rocky but not bad and there is some turtle grass but it isn't terrible and the snorkeling is really good and so very easy.
There are lots of very good dive ops on GC. TNI has made arrangements with DNS Divers to service their guests, but you can do some research and pick the dive op of your choice.
If you stay on 7MB many will pick you up on the beach or in a van and transport you to the marina. If you have a car you may have to drive to the marina to meet the boat. Just make sure that you won't be put on a boat that will also service the day divers from a cruise ship.
There are also some good (and inexpensive) shore dives with onsite dive ops including Turtle Reef, Lighthouse Point, and Cobalt Coast. The Eden Rock and Devil's Grotto shore dives have taken a beating so they would be my last choice. I have heard that the house reef at Sunset House is also the worse for wear but I haven't checked it out.
We love Cayman, have a great trip!