Parking is available at The Crown itself which is free after 6pm. http://en.parkopedia.co.uk/parking/carpark/bowers_row/cw5/nantwich
There are also plenty of other car parks within easy walking distance:
The Bowling Green http://en.parkopedia.co.uk/parking/carpark/bowling_green/cw5/nantwich
Love Lane http://en.parkopedia.co.uk/parking/carpark/love_lane/cw5/nantwich