looking for advice -- pros/cons to renting a car for the day in either Corfu or Santorini - rental car companies you have used -
Renting a car always gives you the opportunity to explore an island at your own pace. Be sure to go to your local AAA office to pick up an International Driving Permit, no test required.
Santorini: Vazeos Car-Moto Rental, Spiridakos Rent-A-Car
I think a car is a very good idea. The fees for a small car are modest and it opens up your visit.
Lee knows Greece very well so check out his suggestions.
We asked the hosts at our hotel (Naxos and Santorini) to arrange it for us and that worked out very well. The advantage, if any, was that the car was available right at our hotel. The rental company also provided us with the necessary permits.
Be SURE and take your camera.
I've never been to Corfu, but it is totally unnecessary to rent a car on Santorini. The local bus system is cheap and efficient and will easily take you to anywhere on the island. There are taxis all over the place if you prefer. A car will be nothing but a major headache for you.