The easiest way to explore the city is a combination of walk and public transport. Public transport in Nuremberg is quite well put together and its even faster way to move in the city then by car. However, if you are moving by car, you will have to leave you car in one of Parking houses (Parkhaus) in the city centre:
Almost every hotel has a secure parking. If you want to, you can always try to find empty parking slot on street, which can become to be an issue. If you have luck and spot one, they are often charged or reserved for hotel or shop guests. If you happen to find a ticket for a wrong parking under your wiper, it’s definitely much better to pay before you leave the city. Otherwise if you come from any other EU country, they will resend it to the owner of the car.