Each owner or lessee of an athletic field, racetrack or place where races of any kind are held, or where admission fees charged are in excess of $.50, shall pay the following license taxes: In cities or towns of less than 10,000 inhabitants, or within five miles thereof, $10; in cities or towns of 10,000 and less than 25,000 inhabitants, or within five miles thereof, $25; in cities of 25,000 inhabitants and less than 50,000 inhabitants, or within five miles thereof, $50; and in cities of 50,000 inhabitants or more, or within five miles thereof, $100. This section shall not apply to racetracks used exclusively by any county or state fair or athletic fields owned or maintained in good faith by educational institutions located in this state. The provisions of this title permitting the payment of a half-year license tax after April 1 shall not apply to this section.