Renting a car in Greece and Italy (first time renting in Europe)

I usually stick to the majors--Hertz, etc. But everyone raves about Autoeurope, which is a consolidator. I'd poke around on Google Maps and see who is represented in the places you will be. I'd assume it would probably be perhaps just a day rental on Santorini? Depends on how long you are there.
In Italy, you need to be aware of ZTL, which is an area in historic towns where driving is restricted. Google it and learn how the sign looks. You typically park outside of an old town and walk in. You might map your routes to see if you''ll be encountering tolls, but driving in rural Italy is easy. Watch your speed, otherwise no worries.

IF there is any question regarding Santorini, I always look first for the recommendations from LEE -- who has visited that island annually for many decades (yes!) and who constantly researches the most reliable resources for newcomers, simply from motivation to give others the best experience. I would absolutely rely on his advice. I clicked on his name and found this advice recent thread regarding car rental (BTW, he usually recommends locally-based resources because of quick action in case of any 'glitch'):

"Some rental agencies will let you drop the car off at the airport when you leave. I've done this twice using Vazeos in Oia. I also recommend Tony's in Firostefani, Spiridakos in Fira and Motor Inn in Kamari Beach."

We usually rent with Hertz because I have a corporate discount card from 15 years ago giving me the lowest prices.

If you intend to rent in Italy, be aware that not every town has a car rental agency. It's usually at airports and in larger cities that you can find rental cars. The optional CDI insurance is mandatory by Italian regulations, but it's reasonably priced. Be aware that they'll try to get you to take a personal belongings insurance in case your luggage is taken--a ripoff.

We were on Santorini for a day, and found it to be a very small, but beautiful, island. We just rented an ATV (4 wheeler) to see the island. They have UTV's and ATV's for rent all over town.

We rented a car from Tony's in Firostefani for a day last May. The price was very reasonable. We stayed in Firostefani so it was about a 10-minute walk from our hotel to Tony's to pick up the car. Mrs. Tony gave us a snack when we returned the car! But I will say that our car was old (not sure of the year). Nothing was automatic. The car had handles to roll down the windows, and you have to put your key into the lock to lock and unlock the car. But that was fine with us.

Tony emailed me several times to remind me that we needed the International Drivers' License; yet they never asked for it. I have a feeling if we were in an accident the police would ask to see it. So definitely get your International Driver's License, which I think is good for a year or two.

We have used AutoEurope for all car rentals for many years.

There are three consolidators often suggested by travel writers: AutoEurope, Kemwel and Gemut. I think there may be a corporate connection between the last two. The word is that it often saves a bit of money to go through one of those three. AutoEurope I think is used the most, at least by folks on this forum, and several have said the company was very helpful when they ran into a problem when picking up or dropping off a car.

I have never rented a car in Europe myself, but if I were to do so, I'd check the rates offered by the consolidators and compare them to the cost of renting directly.

Autoeurope and Kemwel are now the same company. I have used them, starting with Kemwel, for many years. But while in Greece, we used the local agency, Tony's, on Santorini, and a different local agency (Smile Naxos Car Rental) on Naxos. Not sure why I did that. Perhaps the local agencies' rates were lower. Or their offices were close to our hotel so more convenient. Actually, Smile Naxos delivered the car to us at our hotel. So that is something to consider as well.

Are you sure you want to pick up your rental car at the Santorini airport and drive in the caldera towns, Oia, Fira, Firestefani? If you are renting the car for one day, it might make more sense to pick up the car at an office closer to your hotel. Or ask if they can deliver the car to you.

Thank you all for the tips. I booked with Enterprise in Santorini. It was 60€ for a week in March. I booked with Europcar in Bolzano, and it was 662€ for 5 days in June. Kind of a shocking difference, but it is what it is I guess.

I learned that none of the car rental places in Bolzano are open at all in Sunday and only one or two are open on Saturday. It really limits the window a bit. (In case this is helpful for others in the future).