RichardJ,
There WAS such a place about 18 months ago, on Clarence Street between Margaret and Erskine and close to Wynyard Station. Run by Asians I think, we thought it was a pastry and coffee shop at first, but we got eggs and toast, and maybe bacon for what we thought was incredibly cheap. Populated by the locals and office folks looking for a coffee. It is walking distance from your hotel (although mostly uphill)- ask your concierge.