Ideal Santorini itinerary for 4 days?

4 days so you have 5 nights? We spent four nights the first visit and it was too long.
What to see/do? Akrotiri is number one. Amoudi Bay Harbor, have lunch down there. Look at Caldera view.
Hike Oia to Fira or vice versa. Santorini is not known for its beaches.

Even though Santorini isn't the best beach island, I'd go to Perissa Beach, maybe the same day as Akrotiri if you do that. You could also check out the "Red Beach", "White Beach", or "Black Beach" which I didn't do but are near Akrotiri.

I did the boat tour that took us to Nea Kameni (the volcanic island), the "hot springs" on the smaller Palea Kemeni island, and Thirasia island (lunch and a swim or a steep hike up to the town).

I say yes to the Fira/Oia hike if you are up to walking for a few hours.

We did 5 nights in Santorini and it was a bit long, but we did everything..... do what others recommended plus do the Black Beach, you will not regret. It's very very shallow, you walk a mile into the sea and it's still knee high....