Most cruise ships dock at the main port in Limassol, which is about 4 km (2½ miles) southwest of the downtown. This is a vast commercial enterprise, but has dedicated cruise berths and offers a shuttle to the passenger terminal. Here you'll find refreshments, tourist information, currency exchange, and a taxi station. Some cruise ships also call at Larnaca, but at this writing Limassol is the major cruise port.
If you want to explore independently, take a taxi or bus from the port into the downtown. Bus 30 takes about 15 minutes to reach downtown Limassol. Urban taxis have an initial charge of €3.42 (€4.36 at night) and then €0.73 per km in the daytime, €0.85 at night. The waiting time day-rate is €13.66 per hour. Urban taxi drivers are bound by law to run their meter, rural taxis are not, but if you engage a taxi in town it will be classed as an urban taxi.
To travel farther afield, consider taking a service taxi (four- to eight-seat minibus) run by Travel & Express. Service taxis link all major towns for a fixed fee; for instance, Limassol to Larnaca costs €9.90 Monday to Saturday and €11.80 on Sunday. Urban taxis are generally very cheap for local travel, but far more expensive than service taxis between towns. Buses are cheaper, with Limassol to Larnaca a single fare of €3, but they are slower than service taxis.
You can reach many interesting and ancient attractions in the surrounding Cypriot countryside if you rent a vehicle for the day. Car rentals are about €50 for a subcompact manual vehicle. There will be an extra charge for delivery to the port or pickup in central Limassol.