One thing you must have in mind, if you choose Mykonos is that it is an expensive place. So in order to live Mykonos' way, you have to rent a car, at least for one day. That way you can discover the beauty of Mykonos.

The island is beautiful and it is nice to get away from the crowds for a while and explore the villages and the sandy beaches.

You can rent cars through your hotel. If you are going to fly in to the island, there are a bunch of rental offices at the airport (including some of the major rental companies.)

 If you're there in July then A/C is a MUST.  The jeeps don't have A/C, but that will not be an issue for you in September. The jeep is a great option. It is really cool driving around in an open air vehicle!

Driving a scooter in Mykonos is very dangerous due to narrow roads and windy conditions. Keep in mind that every year many accidents with scooters happen in Greek in this inland.  Please, please wear a crash helmet and one that fits properly.  You might stay cooler without them but there's nothing cool about death or serious injury!