The Grand Caymen Island is one of the safest places in the Caribbean, due to the stable economy. Our dollar is valued at 80 cents compared to theirs. The bus system is quite good, but private taxis can be expensive. If this is your first time there, I would take a tour offered from the ship, unless you research it yourself.
Ochos Rios isn't a place I would recommend doing alone, especially if you're not familiar with the customs or area. We were there in November (2000) and felt that Jamacia has done a decent job improving passengers safety. With that said, I would use extreme caution if you explore on your own. Jamaica is a beautiful island; if you hire a cab, make sure you understand the pricing (Jamaican or US currency?), round trip fare or one-way? Also, the vendors are very "forward", but a
"no thanks" usually does the trick. Don't be afraid to negotiate if you find something of interest (they expect it). Have a great time.
John, I agree with the above. My family goes it alone in Cozumel, and Cayman but not Jamaica. Cayman.. we booked a private tour to stingray city, Capt.Laramee. It was Super-Fantastic and was about 1/2 price the cruise line. They have a sign where you can book them at the dock.