Long-term parking near Parker's Piece

Broke friend from back home (North Wales) is staying with the wife and me for a few weeks. We live just off Parker's Piece, and a look at the council website tells me that the Grand Arcade car park and the two Grafton ones are short-stay only. Is there anywhere within, say, a mile of Parker's Piece where one could park for a week or two without breaking the bye-laws and the bank?