The graffiti included tagging and rude words inappropriate for young children to see, Ms Meijn said.
"Inside the tower there's a lot of rude words and a lot of little kids play there. It's just not right."
"It's literally everywhere."
Tagging at the park was not a new problem but was particularly bad at the moment, she said.
Each tag costs an average of $80 to remove.
Police patrol the area several times a day but would be looking to increase foot patrols, as well as working with council to improve security and lighting, she said.
Other areas frequently targeted by taggers included the Briscoes carpark and wheelie bins in the central business district.
Chairman of the parks and open spaces task group, councillor Gary Caffell, said the council would be looking into possible solutions to decrease vandalism in the area.
"We do have a programme where we look to get rid of it as quickly as we can but it's a constant problem and at this time of the year it tends to get worse. It's something that we are forever trying to clean up and it's very hard to get rid of it - they come back and do it again."
Mr Caffell asked the public to contact police if they noticed anything.
"I personally can't understand what kind of thrill anyone gets out of doing that kind of stuff. It's beyond me."