We would like to know about this as well.
Did a quick look around and found the tidbits below. We used mass transit in Vancouver easily but suspect the islands are quite different.
Do exercise caution with taxis or buses. Be very clear about destination and price as well as pick up times.
Cayman Islands Taxis | caymanislands-guide.info
Grand Cayman Islands - Taxi Service
We might have to check out the pedicab here...
WHEELS - Cayman Pedicab Services
"The local public buses leave from the library on Edward St. They are like VW buses and sit up to 10 people in a pinch. The cost runs up to $2-3 usd to go about Grand Cayman. They all have blue license plates to identify them by..."
"Long rows of cabs are waiting on Harbour Drive located adjacent to the cruise tendering area. The cabs are mostly new, clean and safe. Best of all, most have fully-functioning air conditioners. Fares are determined by destination per person. The amounts are given up front so there will be no surprises at the end of the trip.."
"I would recommend a taxi if you've only got a short time (ie arriving/departing via cruise ship).."
"The best way to get around for those on a budget is the bus.
They are in fact mini-vans and don't really have designated stops (exept its departure point).
You can find the bus just behind the Library in George Town.
They are quite frequent, efficient, not expensive and a good solutions for those who stops on Grand Cayman during a cruise. "
Phil & Liz