The public transportation system in Cape Town is not very well developed. Some new bus lines throughout the city have been build in recent years but the network is still not very dense. Many locals use the group taxis - old vans that cruise the town and pick up passengers on designated places or just about anywhere. These are not official taxies and for safety reasons most whites do not use them. It is not unusual that a taxi for 9 passengers drives around the town with twice as many people inside. Collisions of these taxis are often fatal.
Licensed passenger car taxies are available at most touristy places. Make sure that the driver turns on the meter and check the approximate fare before you enter the cab. Individual taxis are not cheap but reasonably priced. Hop-on hop-off busses will take you to the most popular places but run only during the day.
Rent a car at the airport if you want to be flexible. Driving is on the right side of the road like in Great Britain. Drive carefully if you rent a vehicle. There are my un-roadworthy vehicles on the roads and some drivers are a bit unpredictable. Expect sudden breaking of a vehicle driving in from of you, unexpected change of direction without indication or vehicles with only one or no lights on at night. Watch out for pedestrians on the roads.
You can rent a vehicle at one place and drop it off somewhere else if it suits your itinerary. This is at a surcharge and not all car rentals offer this service. Arrange a vehicle renal beforehand if you plan to visit Cape Town during the high season which start in November and end in March with its peak in December.
These are big car rental companies in Cape Town:
Value Car Hire (www.valuerentalcar.com)
Budget Car Rental (www.budget.co.za)