...I want to feel safe with my surroundings...Yes I know, you can't beat Cozumel's pricing OR Bonaire's diving...I've been to the sister islands of GC by small plane but it's a new world now...
I think the Caymans are comparable (or even better) than many other Caribbean dive destinations. Some of the walls are spectacular, especially around Little Cayman. It is only the abundant shore diving and unique diving culture that makes Bonaire such a special place; but yet there is that persistent "petty theft" problem that makes it a little less special in my opinion.
Cozumel is less expensive and has wonderful diving, but sometimes you get what you pay for, especially since you mentioned safety. My husband and I have both gotten nasty gastrointestinal illnesses when vacationing in Mexico even though we always take precautions, and the risks of mosquito-borne illnesses like dengue and chikungunya are much higher there than in the Caymans - where they have good mosquito abatement programs and the food and water are safe to eat and drink.
As far as personal safety, I feel safer in the Caymans then I do nearer to home; the crime rates are low, the people are polite and friendly, and just about everyone speaks English. Of course, you should stay alert and use common sense wherever you go in the world.
I love all 3 of the Cayman islands and it's great that you prefer GC, but I don't understand your "it's a new world now" comment? It will cost me $140 US roundtrip to fly to Brac from GC and back this fall, that is hardly a deal-breaker when you consider the expense of a Cayman vacation; especially if you don't mind the costs of eating out.
Ask your dive op about the shore dive options on GC, I am sure that they can advise you; but stay away from Eden Rock and Devil's Grotto when the cruise ships are around. And I would expect my dive op to avoid Stingray City and most of the West side boat dive sites, including the Kittiwake, during peak cruise periods, too.
We like to rent a car and explore because there is a lot to see and do on GC, but I do recommend bringing a GPS with you. We find it helpful when negotiating the roundabouts and the streets of Georgetown. We bring a Garmin GPS and car-charger with us. Garmin has the best maps of the island IMO.
The link to Tsetudo's snorkeling guide is below; there's very good snorkeling from shore available on Grand Cayman and it is free and easy. We prefer diving in the sister islands so when we are on GC we tend to snorkel, shore dive, and do a few boat dives; but you can find great diving around all of the Cayman islands. Have fun!
http://snorkelblog.tumblr.com/
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