If you look at it one way and group the different companies that offer parking, it could be a monopoly as that is the only place you can park. On the other hand, the different companies offer different prices and consumers can substitute.
If there are different companies offering with different prices, but not so many companies that it is perfect competition, then it is monopolistic and not a monopoly.
This depends on how you define the good in question, which is a typical problem when talking about market structure. If the good is "parking at the airport " then it's probably a monopoly since most airports manage their own or through a single contractor on their property. If the good is "parking for the airport" then you have firms providing the product off airport property and there is some competition though they may differentiate through covered parking, shuttle services, etc. In this case it would be monopolistic competition.