Sometimes it pays off to reserve a car ahead of your arrival on an island, even if it is just for one day. This way you can quickly get a good impression of an island as a whole and take a look at many places. Who knows you might find something really nice. I don't get the impression that there are a lot of car rentals on the island (the island isn't that large and there really aren't that many kilometers of road), but I did find this one: Glaros rent a car in Gialos. They say that they are based in the harbour at a few meters distance of the place where the ferries come in. If you really want to be assured of a rental car when you arrive at Symi (for instance in high season this might be wise) than you could try to reserve a car.
Τel.: 0030 22460 71926 & 71713 Fax: 0030 22460 71926 Mob: 0030 6948 36 20 79 - Send an e-mail to Glaros Rent a Car in Symi.