my .02
Must do boat dives: Trinity Caves, Big Tunnels, Orange Canyon. (deeper dives)
Must do shallow boat dives: Aquarium. Also Stingray City one afternoon - most fun you'll ever have in 15'.
Must do shore dives: Turtle Reef. There will often be Tarpon schooling in the afternoon in an overhang just to the south of the ball. Also some of the larger fish use it as a shortcut between the North and West walls, we saw a group of Eagle Rays go screaming overhead. It's a pretty shallow dive, only 50' or so at the base of the reef but filled solid with stuff all the way down. And you can also go out across the sand to the wall but it's not as spectacular there as it is farther north.
And get your picture with the Mermaid at Sunset House (53' at the base). Sunset House also has the Cathy Church Photo School/Gallery in the basement of the main house and My Bar which is a diver's bar. We spent a really pleasant afternoon there.
I've read Lighthouse Point is another really good dive. It's been recently staffed by Divetech. It's in the same area as Turtle Reef.
Plan your day around staying out of Georgetown if there's cruise ships in port. The sidewalks are over-run with cruisers who are oblivious to cars approaching from the opposite direction. And traffic is a big mess.
If you plan to dive Eden Rock/Devils Grotto, do it later in the afternoon. If there's 3 ships in port, the third one is positioning on thrusters so the viz will be down. Although I didn't think it was all that great of a dive, it's been dove by cruise ship divers for decades and was pretty tired looking, lots of broken coral and ship debris. And the dive seems to end in about 40' of water, after that it all appeared to be sand. Not that you'd want to go farther, there were jetskis and two cruise boats moored past that. I guess the Grotto is better - we didn't dive it. Certainly nowhere near their claim of 2nd/3rd best dives in the Caribbean.
If you're all 25 or less dives, tell the diveop when you book. Typical GC dives are the first dive is deep - 100' or so down the wall followed by a shallow 2nd dive. But they can/will tailor it to the experience level on the boat. The way the wall angles and drops off in some places there's not a really good shallow alternative except hovering in the water column. Also watch your depth, the water is so crystal clear that you can get deep fast without realizing it. One time my buddy and I were on a planned 80' dive, when I noticed him above me waving me up, I then realized I was at 122'. And the bottom was another 1000' or more - we were diving off the North Wall. Ooops... At Big Tunnels I looked up from about 105' and could clearly read the Scubapro "S" on the hookah reg on the safety stop bar 90' above us.
If you stay on Seven Mile Beach, most of the boat-based diveops - which is the majority - will pick you up streetside anywhere along there. At almost every shoredive site there's some sort of dive/resort or dive facility and you're required to rent tanks from them to dive there as they legally own the property down to the waterline. Most won't let you remove them from the property also. Should you need tanks for an open shore dive, the divestore in West Bay rents them.
Other things to know: Cayman is wicked expensive. The dollar is .80 to the CI$. A typical meal in a restaurant can be upwards of $40. Even KFC was pricey...lol. Food prices in the markets are high also and liquor is stupid expensive so BYOB if you're planning to drink alot. We rented a condo and did some cooking to keep the costs down. Also just about anywhere - except maybe around the Ritz-Carlton, you're going to want a car as it's a walk to restaurants, shops etc. And there's some good restaurants in/just north of Georgetown also but no one stays there - except for at Sunset House.
hth,