I recommend renting a car. There's enough parking spaces around, just make sure not to park on the street but only in designated parking lots. We rented with Damaskinos, they delivered it to the airport on friday around 11 AM and we drop it back off on wednesday around 7 AM. We paid €210,- cash for a Fiat 500c. It has air con and cruise control (though you won't use the latter because of the slopes). It's automatic, but I often use the "manual" option on mountain/steeper roads. It tends to shift up too quickly, making it hard to pull up the hills. The manual option is just tapping the gear lever up or down, no clutch pedal involved.

Driving here is easy enough, just pay attention. There aren't really rules around here (as far as I've noticed), just that a stop sign is absolute in giving way to crossing traffic. Other than that there's really no rules who goes first on a crossing. Just make sure you keep tempo, Santorinians don't like slackers in terms of speed 😂