I've rented from Hertz in Greece once, on the Island of Crete. Very professional and reliable.
There are many local rental companies everywhere on the islands that rent tiny cars by the day, but they will hassle you hard in case of any small scratch.
Greece is included in the rental insurance coverage by a US-issued credit card.
Very few countries are excluded (Ireland, Italy, Israel, Jamaica, and a couple of others I don't remember). There is no point in buying CDW from Hertz. All you have to do is decline coverage (the mandatory liability is included in the rate). When you make a reservation with the US residency, all the other coverages are optional and not included in the quote.
The island of Santorini is very tiny, there is no point in renting a car there at all.
The cars with automatic transmission are priced a lot higher than the manual ones.