Dive Turtle Reef - it's one of the better shore dives. It's located at the Cracked Conch/Macabuca restaurant in NW Point. Sundivers is on-site. Sunset House is a good way to spend an afternoon, dive the Mermaid, view the Cathy Church Photo School gallery and have lunch/drinks at My Bar. Stingray City is worth doing once.
A lot of the shore dives have on-site operators for tank rentals etc. Since they own the property to the waterline you rent from them. Cobalt Coast, Lighthouse Point, Sunset House, Eden Rock all do this. If you plan to do any independent shore diving (Cemetery Beach, Smith's Cove etc.), tanks are available at Divers Direct in West Bay or Eden Rock downtown. Most of the dive operators are either boat based or won't let you remove tanks from their property.
Ambassador Divers and Neptunes also get good reviews here often. If you stay along Seven Mile Beach many of the dive operators will pick you up. Some of the resorts have on-site dive operators also. Ambassador is located at Comfort Suites for example.
Don't go downtown when you see the big ships in the harbor - unless you really like crowds.
Driving is on the left - the tourists downtown don't always get it. We've had several step off the curb right in front of us. Finding an ATM won't be a problem either...lol - there's like 300+ banks on the island. You may need one, everything on Cayman is pricier than just about anywhere else I've been. IIRC the exchange is something like US .80/CI$
We rent cars at Andy's. They're at the airport and have an office on SMB. They used to pick you up also - probably still do. We didn't get a car immediately since we had a late flight and were boat diving the next several days.