Is there a car service for a hospital or clinic visit in Wellington?

Yes, and it is a different job from an airport run, so it is worth saying how it differs.

The car waits. A consultation that was meant to take an hour takes three, and nobody wants to be ordering a ride from a waiting room or explaining to a stranger why they are moving slowly. The chauffeur stays, and the fare was agreed before the day started, so the waiting is not a meter running.

Pickup is at the door rather than the car park, and the chauffeur will walk with you if that helps and stay in the car if it does not. Nobody asks what the appointment is for. It is not written down anywhere beyond the address.

For a course of visits over weeks, the same chauffeur each time is usually the right arrangement — by the third one it is simply a familiar face on a difficult morning. From anywhere in Wellington, the show grounds, the polo grounds, the village, or straight from PBI for someone flying in to be seen.