Sec. 12.1. Authority to regulate off-street parking.

   The city council shall have power and authority to enact ordinances for the regulation of the use by vehicles of:

   (a)   Municipally owned or leased off-street parking areas and facilities;

   (b)   Publicly owned off-street parks, outdoor recreation areas, and yards and grounds occupied by public buildings; and

   (c)   Privately owned areas permissively used by the general public for parking or street purposes.