Could you be more specific - how many dives do you want to do per day or week? Do you want to be at a place with a dive op onsite are you okay with being picked up by van or on the beach by boat? Are you also interested in shore diving? Are the non-diving members of your party interested in shopping, restaurants, and other entertainments or are they mostly looking to enjoy nature and relaxation? Are you okay with renting a car and driving on the left? What is your ballpark budget excluding airfare?
Grand Cayman is usually the best choice for mixed parties of divers and non-divers, because there are lots of things to enjoy topside and the Seven Mile Beach is a gorgeous destination. But 7MB is a very developed area and there can be traffic and congestion, but renting a condo as
@Divetech Cayman suggests is a good way to find a quiet place on the beach.
Eating out can be very expensive on Grand Cayman, so renting a condo or house also allows you to prepare some simple meals and then go out for a great meal about once a day. Having a car gives you options regarding where to stay and places to eat and visit. But if you don't want to rent a car then you should stay in central 7MB although that is generally considered to be the most developed and expensive area.
What time of year do you plan to travel? 7MB is on the West Side of GC and that side is generally the most protected from winds and it is often the area when you will find the calmest diving, especially if you are traveling in late fall and early winter when the winds can be a problem. Most of the shore diving is available on the West side.
There is usually lots of sea life on the West Side but not always the best reefs. The most dramatic walls are on the more remote North Wall and the East End but the winter winds can limit access (especially on the North Wall). You are most likely to see sharks on the East End but you will be distant from many of the popular tourist attractions.
Some of the best Cayman diving IMO can be found on the Sister Islands of Little Cayman and Cayman Brac. They are a short flight from GC and there isn't much to do besides eat, sleep, relax, dive, and enjoy nature on LB and CB.
Little Cayman's Bloody Bay Wall is spectacular, the reefs are close to shore and start shallow, but if you travel during rough weather you may need to dive the more protected south side of the island, and that is okay but a bit disappointing.
Cayman Brac has beautiful walls and reefs and may offer more options to dive other sides of the island depending on weather (like Grand Cayman) but the reefs start a little deeper and are not as spectacular as LC. The Brac Bluff is a gorgeous cliff rising high above the sea and there are opportunities to hike and climb and go caving on CB.
When we stay in the sister islands we prefer an all-inclusive resort like the Cayman Brac Beach Resort and the Little Cayman Beach Resort because there are few restaurants and shops and the food prices are quite high. These 2 resorts are on the beach but they are not good swimming beaches, but they have pools and the CBBR has an outstanding infinity pool. Both resorts have dive ops and small spas onsites and we have found the food to be abundant and excellent at both places.
My guess is that your first trip to Cayman with non-diving companions should be Grand Cayman, but please give us some more info and we may be able to suggest the best options for your needs.