Traffic moves slowly, with refreshing courtesy and on the left. You can take a taxi anywhere on Grand Cayman, though availability drops off the farther you get from George Town. Taxis are not available on Little Cayman or Cayman Brac. You can take a ferry between North Sound and Rum Point on Grand Cayman, which takes about 40 minutes each way. The Caymans are flat and small enough that getting about by bicycle is feasible, so long as you're not ferrying scuba gear.
Bicycles are available for hire.
Short of chartering a private boat, the only way to get from Grand Cayman to the sister islands is by air. Island Air flies small prop planes to Cayman Brac and Little Cayman in about half an hour. Cayman Airways flies 737s to Cayman Brac but doesn't offer a service to Little Cayman. Gerrard-Smith Airport is located at the western end of Cayman Brac. On Little Cayman, Edward Bodden Airfield is located just west of South Town, on the southwestern coast.