The city is not considered dangerous, but keep in mind that you are in a place full of visitors. Taking basic safety precautions (keeping an eye on your belongings, locking car doors, and so on) is perfectly sensible.
In tourist areas, especially near the train station and at the Christmas market, it is advisable to stay alert — petty theft can occur. Otherwise, Nuremberg is a calm city with a high level of public safety. Street lighting works well, and the police respond quickly to calls, so you can feel quite safe both during the day and at night.
