BYELAWS could be brought in to stop people climbing the sculpture dubbed 'The Rusty Comb' outside Barnsley Town Hall.
The council also wants byelaws to prevent people polluting the fountains, and those breaking the rules would face a fine. Barnsley Council's ruling cabinet will consider the rules on Wednesday.
The report outlines proposals to prohibit anyone climbing on, or hanging from the sculpture in the new square.
There would also be a penalty for anyone polluting the fountains with washing-up liquid, washing powder, bubble bath, detergent or other substances.
It said many enjoyed using the new facilities but a few had already started to misuse them. BMX cyclists and skateboarders treating the area as a skate park had caused damage to stonework, benches and plants.
Having had two people scale the sculpture's heights, it was inappropriate to apply anti-climb paint to the sculpture, which is on loan, because of its international importance.
Other measures put forward include CCTV surveillance, warning signs, patrols of the area, and work by a 'town centre ambassador'.