If you want to see the town, forget about car rental. The town is very small, the streets are very narrow, and there is no place to park. Other than tiny 3 wheeled delivery carts and mopeds, I didn't see any other cars in the town. The fun of Mykonos is wandering the widing streets and exploring, finding little shops, restaurants, etc...
You may want a car if you wish to skip the town and drive around the island, but I didn't see any rental places at the port. Good luck with it.