I've just returned from our 8th trip to the Cayman Islands, we have been taking recreational vacation dive trips for a long, long time - primarily in Florida, Bahamas, and Caribbean and Central America, but we have also ventured to a few other areas like Hawaii, Red Sea, and Baja - I wish that we had traveled further into the Pacific but alas, so far we have not.
Cayman is one of our favorite destinations, but it wasn't always that way. We loved the diving but money was tight and it is an expensive destination, plus we didn't care for all the touristy stuff that we found on Grand Caymam. We kept resolving not to go back but we kept going back, every several years. It wasn't until our 3rd trip that we gave in and decided that we really love the Caymans - but that's when we discovered that there are actually 3 Cayman islands! And that Grand Cayman offers some lovely places to stay away from the crowds and expense of George Town and the Seven Mile Beach.
I now love all 3 Caymans Islands! Since the OP said that this trip was primarily for diving I want to suggest that he also consider the sister islands of Cayman Brac and Little Cayman - fabulous diving but not much else to do. Or take a look at a liveaboard trip on the Cayman Aggressor - that gives you the chance to dive the best sites off of all 3 islands - and absolutely nothing else to do!
A liveaboard seems like an expensive option, but it includes everything except tips and airfare. And the Cayman fleet is offering their Anniversary special right now, so you get 34% off each trip but you have to book quickly (by Nov 24!) and you have to travel by the end of April, but the OP was talking about May so that might be an option.
A liveaboard easily gives you 4 to 5 dives per day and includes specialty dives like night dives and the Kittiwake, and sting ray city. And if you wish, you could plan to stay a couple of days extra on GC, to enjoy the beach and the amenities. Some people love LOBs and others do not, it is a personal preference. I always feel that LOBs give you the easiest, best diving but the living accommodations can be cramped and limiting! But who cares? You are there to sleep, eat, and dive!
One word of caution, the Cayman Aggressor has a rather different venue then most other liveaboards, many of the dive sites they visit are accessible from shore. The advantage of the LOB is that you can do a lot of great diving off all 3 islands. However, the Aggressor will not make the crossing from GC to the sister islands if the weather is bad. In that case, you will be stuck on a boat off shore of Grand Cayman wishing and that you were in a bar on shore! They do make the crossing most of the time, around 75% I think, but they aren't always able to make it.
Here's another (land-based) option. The Clearly Cayman (Tibbetts Family) Resorts are offering specials through mid April at their resort on all 3 islands, so there are many opportunities right now to dive the Caymans at more reasonable prices.
When we are on Grand Cayman we usually stay in Bodden Town at the Turtle Nest Inn. It's lovely and reasonable and the price includes a car rental. It is centrally located and not too far from anything. Bodden Town is not a resort area, more residential, but it is on the beach (not the Seven Mile Beach!) but very nice with good snorkeling right outside. But you have to be willing to drive on the left side of the road!
Nowadays we mostly snorkel and shore dive on GC and wait to get to either Brac or Little to focus on boat dives - but if you want to do a lot of boat dives, you could stay on the East End at Compass Point, or you could stay on the West Side, north of 7MB and dive North and West with many of the island's dive ops.
When we go to the sister islands of Brac or Little we usually stay and dive with the Clearly Cayman resorts. Very nice, all-inclusive (except drinks). You only get 3 boat dives a day on Brac or Little but they offer night dives a couple of nights per week, and they will rent tanks if you have the energy left to shore dive, but you will need a car. Their resort on Grand Cayman (Cobalt Coast) offers 2 boat dives per day and unlimited shore dives on the house reef but sometimes they get winded out for the shore dives. You will also need a car for CC.
Anyway, there are lots of options with the Caymans - and they aren't all ridiculously expensive, and if the weather cooperates you can find some wonderful diving!
Take a look at the links below and let us know if you have questions!
The differences (for a diver) between the 3 Cayman islands - Cayman Islands Forum - TripAdvisor
7-Night New Year Dive Vacation Starting at $1,395*
The base prices are for 2 daily dives and 2 meals, but you can upgrade
Aggressor Fleet's 34th Anniversary - 34% OFF - Book before 11/24!