I understand that staying in city Center with a car is not a good idea. What would be a good area to stay in outside the city Center
You can stay wherever you want, even in the center. Depends by your needing. Staying in the center allow you to go out in the evening without needing to drive again. The most of hotels have a parking lot in the center and if the hotel is within the ZTL telling the plate car number you are authorized to reach the hotel without being fined.
We enjoyed the Best Western Liberta Hotel in the center of Modena. They have parking available for a nominal fee.