There is limited parking at the venue with the entrance off Cashel Street but there is plenty of carpark buildings nearby.
This is the Hereford Street view of the YMCA (right), the campervan is in a 5 minute drop off, the blue wall is a mural on the end of the Papa Hou, and on the same side of the street, beyond the big tree is Wilson's West End Car Park. The old building on the left is the Christchurch Arts Centre.
The address for the West End Car Park is Hereford Street, but that is the exit, you enter from Cashel St. It's $6 per day on Saturday and Sunday and $6 for Friday night. (The hours of operation means that is when you can drive in but you can drive out any time.) You can only come in and out once for that $6 though, if you leave and come back you will be charged again.
On street parking in the area is limited and expensive. There is a 5 minute drop off zone in front of the main entrance, which looks in frequent use. Every day the metered parking (which uses your number plate, not paper tickets) is $3.10 per hour with a limit of 2 hours between 9am and 6pm.
There is some parking behind the YMCA off Cashel St, but it has a 2 hour limit as well. Visitors coming for a short time or only in the evening could use a space here (no charge) but must write their registration plate number on the register on the YMCA reception desk. There are also some spaces reserved for a Medical Centre adjacent on Cashel St, so don't park there.
View of the entrance to the YMCA from the car park at the back of the building.