Arguably the best shore dive on the west side is Turtle Reef - a few mins drive north of SMB. Sundivers is on-site for tanks - Ollin shares space with Cracked Conch so has some info on their website.
Nearby is Lighthouse Point another good dive. Divetech is there and they also boat dive from there or nearby. One they do not to be missed is Ghost Mountain but almost all the dives in that area are good since a lot of them are off the North Wall. A little farthereast is Cobalt Coast - Reef Divers is there.
Dropping down SMB - Cemetery Beach is a good snorkel, or really shallow dive. Most boat operations will pick you up at most resorts/condos along SMB - boats are kept in one of several marinas behind it. Evreybody has their favorites - mine are Anbassador Divers, Indigo Divers or Neptune's Divers. There's not a bad choice due to competition. Good dives in the area include Orange Canyon, Big Tunnels, Aquarium (shallow 2nd dive) Trinity Caverns, Heoo's Wall/Arch and about 50 more. Some of the North Wall is less diveable in winter so the boats move west.
Then down in Georgetown Eden Beach is OK but suffers from decades of being 50 yds. from the cruise port. Cheeseburger Reef is another dive in the area - off Lobster Pot Dive Center which books Wall to Wall, Deep Blue or Off the Wall
Don Fosters sits on the end, their shore dive is Devil's Grotto which is connected to Eden Rock. They have most of the cruise contracts.
A few minutes south is Sunset House - there's 2 shore dives there - or one long one. The Mermaid in 55', a small wreck farther out and a shallower wall even farther out. It's a dive resort, has a good outdoor restaurant and the Cathy Church photo operation on site.
Another few minutes south of there is Smith's Cove a locals beach with a shallow dive. No facilities there so rent tanks at Eden Rock - most of the other shore sites don't allow removal from the property..
There's no shop near Bodden Town. Or any shore dive I'm aware of (it's pretty shallow) My buddy used to stay there annually and drove out to Ocean Frontiers to dive, it's on the south side of the East End. Or back to Georgetown. The dive to do with OF is called Babylon - it's on the north side and I've seen it listed on a top 50 dives in the world lists. If they're not doing it when you;re there try Tortuga Divers on the north side at Morrittt's.
As far as dive sites - there's over 365.
www.idivecayman.com lists many with videos. The Kittiwake is the signature dive wreck - put down as a dive a few years ago and Stingray City the best 15; dive there. It's a lot of fun. I've done about 1/2 of these if you want a short list -
Top 10 Dives - Wall to Wall Diving
pick a diveop you like from the list:
www.cita.ky