The East End and the North Wall are some of the best GC boat diving IMO; but some of the best shore diving is on the West Side but north of Seven Mile Beach; so keep that in mind when selecting a place to stay and dive.
Most of the dive ops are on the West Side and 7MB and they will dive the North Wall when the weather permits. If you stay anywhere in the 7MB area, the dive ops will pick you up in a van, or on the beach by boat.
There are many high-quality dive ops and even the larger companies are okay because they have big boats. You will want to make sure that you won't be put on a dive boat with cruise ship divers but that rarely happens. There are smaller ops available too - we like Cayman University Divers.
If you are mostly visiting GC to do a lot of boat diving then Compass Point and Ocean Friends divers on the East End would be a good choice because you can get 2 or 4 good boat dives per day, but you will be far away from the attractions of George Town and the Seven Mile Beach. You will also be far away from most of the shore dives.
When we are on GC we are there for snorkeling, shore diving, some boat diving, and to enjoy the restaurants and attractions of the island. We usually wait until the second week on one of the sister islands to do most of our diving. We like to stay away from the crowds and higher-priced properties and rent an apartment or condo so we can cook some of our own meals to reduce costs.
If you want to enjoy island's attractions and restaurants but also go diving, you may want to stay in the 7MB and West Bay area, but that is the most populous and expensive area. Sunshine Suites is a popular spot, you will have a kitchen and can prepare some meals and you will have access to the amenities and beach at the Westin across the street - but there will be a daily resort fee added.
Coconut Bay and Lighthouse Point are on the west side but north of 7MB on ironshore. They both offer condos and good house reefs - but I think that they only rent big condos (2 and 3 bedroom) and that won't work for us; we just need one bedroom.
Cobalt Coast is also a remote location, it is on the west side but far north of 7MB. (Up near Hell - don't go to Hell!) I have never stayed at CC but they offer 2 tank morning dives and unlimited shore dives on the house reef, but I understand that the reef is good but it is a bit of a swim. It can get winded out pretty easily up in that area but I don't think that it will be a problem in June, mostly in fall and winter.
The CC resort was recently acquired by ClearlyCayman, the family-owned company that also owns the Little Cayman Beach Resort and the Cayman Brac Beach Resort and Reef Divers is also the onsite dive op. They offer an all-inclusive package but there are so many places to eat on GC and good grocery stores that we have never tried it.
Sunset House is a popular dive resort. It is south of 7MB and south of George Town, but not far. It is on ironshore not beach and breakfast is included but there are no cooking facilities, just hotel rooms. They have onsite restaurants and you are close to George Town's restaurants. Cathy Church's photo studio and shop are on the property if you are interested in photography. You get 2 boat dives and unlimited shore dives but the house reef has gotten beaten up over the years. They may primarily dive the West side, I'm not sure. I don't know how often they go North or East to the best dive sites.
@Trailboss123 could tell you more about diving with Sunset House.
We like to stay in Bodden Town, a residential area south and east of George Town. We stay at the Turtle Nest Inn which is a nice property at a good price and we have full kitchen facilities. They have a nice little beach but it is not the 7MB. The entry is a little rocky but not bad and there is turtle grass, but there is good snorkeling right in front of TNI. A rental car is included and you have to be willing to drive on the left if you stay in a more remote location.
As much as we love TNI it is probably not the best choice if you want to do a lot of diving on GC because you will have to drive to the dive boat; but if you do stay at TNI you could drive East to dive with Red Sail at Morritt's or Ocean Friends at Compass Point, it will be a bit of a drive but on good roads and not much traffic. Driving to George Town and 7MB/West Bay during rush hour is not fun!
So there are a lot of choices on Grand Cayman and it is a pricey destination. A lot depends on what you'd like to do and your budget.
There is an extra charge per tank for Nitrox in Cayman. The Clearly Cayman resorts were offering free Nitrox and free Nitrox certification over the holiday, see below. I don't know if they will be offering it again.
Free Diving, Nitrox, and Nitrox Certification*