Only special permits allow you to drive in inner zones. You mark the date and time, and display it on your wind screen. Otherwise, parking spaces are scarce, and are mostly located within paid parking lots. Driving your own car may therefore not be the best option. Taxis are allowed in most areas and they are numerous, easy to get, and relatively inexpensive.
Private taxis are often much more expensive.
Taxis are cheaper when ordered by phone. Cracovians normally have a collection of these for different taxi companies.