On Cayman Brac, I've been using DDDD's for the past several years. Some of their cars can be a bit "run down", but for the past few years, the ones we've gotten have not only had both headlights working, but the interior dome light was functional.
DDDD's: (345) 948-1599 Just over US$200/week.
For Diving, the options are fairly limited. The standard hotel-affiliated dive operations are Reef Divers & Dive Tiara.
Winston's operation, Brac Aquatics is gone.
Dee's "Village Scuba School" generally either does local shore diving, or hitches a ride on Reef Divers. Dee doesn't have her own boat, partly because the Government restricts the number of licenced dive operations.
Finally, an "unofficial" (as best as I know) "private charter" dive operation is Bunny (a former Divi DM Bunny) working with another Braccer, Shelby Scott. I've dived with Bunny when he DM'ed at the Divi and know that he's OK. I've probably met Shelby, but can't place him at the moment. Bunny does have a regular job (fireman), so you'll have to make arrangements with him ahead of time. His contact info is: email: <cybbline@candw.ky>, or by phone at (345) 917-1558 or (345)948-0254. The one dive report that I've heard of them commented that the rates were somewhat ambiguous, so get your agreement down in writing. Also, because its apparently a private charter, the number of divers necessary for break-even vs. the Hotels is 4-5, so if its just you and a buddy, you're going to be paying a premium if you choose to go this route. FWIW, I'd also ask if their boat contains O2...
Finally, be aware that the long distance telephone rates to the Caymans are as a rule of thumb, expensive. I forget what the current rates are, but I believe its still well over $1/minute.
-hh