Not a fan of the proper game but I do enjoy the driving range. I know some people jokingly say 'just play minigolf' but that's missing the 'punt a tiny thing really fucking far' part.
It's the same thrill as any other game or sport. Many enjoy the challenge of trying to do something difficult and get better at it, and then enjoy doing it competitively, and/or cooperatively with friends.
In the case of golf, you also get the added enjoyment of it being a generally slow paced activity, usually done on a beautiful day in a pretty area with lots of grass and trees.
For me there's a certain amount of stress relief when I feel good contact with the ball. It can also be fun to try to be accurate the same as with other games like darts.