Ideally, you should spend 10 days (9 nights) in Santorini during the high season so you'll do all the things you'd do above, plus: movie night at the Kamari Open Air Cinema. Spend 2 days in Perissa/Perivolos beach.
Is 4 days in Santorini enough?
Santorini is a bit bigger than most people expect because it's not only Oia. The rest of the island and especially the south, is very worth exploring as well. You can spend a weekend to a full week in Santorini without getting bored, so a 4-day trip is the perfect duration.
Do I need a car to get around Santorini?
The bus network heads to several spots on the island and itineraries are frequent, especially during the summer. You can reach all touristy destinations via bus. However, if you wish to explore the island and discover the hidden gems of Santorini, a car rental is the option that will meet your needs the most.