Staying in May, should we get a car to better move about the island?
Yes, and be sure to go to your local AAA office to pick up an International Driving Permit, no test or membership required, for $15. Bring 2 passport photos to save a few dollars.
Better check with your hotel to confirm there is parking nearby it can be very tight in that area. If parking is a problem then consider renting for a day and returning the car to the rental agency, they have parking.
They do have free parking at the place Hotel Mylos, and I just got the IDP from local AAA for $20 + photos was $32 total.
Will we use the care every day? We can walk to Fira, but Oia, historical sights and the beach's seem to be a bit to far to walk.
We will be there for 4 nights.
I paid $15, maybe because I'm a member.
There's a lot to see and do on the island but no one can answer for you if you'll need it every day, as that depends on how much of it you want to experience.
For under $50 a day, it could be worth renting one. I think we may take a taxi from the airport to the hotel and rent the following day for two days, then take a taxi to the airport on the last day.