Grand Cayman, without a doubt, is very safe. You will be fine, everyone on the island is very friendly and it almost feels like you are in Miami. On the Cruise ship they made a big deal about how good the shopping is there, but I found it to be extremely over priced. I would highly recommend going to Sting Ray City, it is absolutely amazing!!! Also, don't miss out on the Tortuga Rum cake. Have fun!
Grand Cayman is safe. When I worked there we never used to lock the house door or the cars....and I fell asleep many a time on the beach, watching the stars and after too many Coors!!! However, we wouldn't venture up to the top of West Bay at night . The main car rental was Coconuts, but I'm sure there are lots around now. They charge you extra to issue you a temp drivers licence, which they do at the rental shop. Just produce your own country one, you also have to be 25. I would say a days rental plus licence would be about CI$25. Remember the road system is British.
Like the others said it's very safe on Grand Cayman.
When you come ashore you got to walk to the left for a little while, then you'll have the opportunity to rent scooters across the street, or walk a little bit more further to rent a car. You can't miss it.
Sailed on :
La Palma, Amerikanis, Southern Cross, Azur (2),
Bolero, Calypso (2), Carnival Victory
Very Safe... it's actually my favorite port. I hate being hassled to buy things and this does not happen here. Plus the Locals are great! They come right up and talk to you. We actually met a man that use to live in detroit that now lives there and he told us it's like night and day. I would definantly recomend doing the stinray tour. We used Soto's and loved every minute of it!