Here are ten, roughly in the order I would spread them over three days. A few are half-day plans, and the boat wants a clear day rather than a fixed slot. If you would rather not work out the ferries and the transfers yourself, a Santorini tour hands the moving parts to someone else.
1. Walk the Fortress Village of Emporio
Emporio is one of the oldest villages on the island and one of the most authentic, and you can see why from the lane you arrive on: white Cycladic houses packed tight against each other, with a medieval fortress folded into the middle of them. The settlement is a maze by design, lanes turning back on themselves and opening into courtyards you did not see coming.
Aim for the fortress, which dates to the fifteenth century, and walk into it rather than around it. Then let the lanes take you where they want. The village rewards the person who stops photographing the view and starts photographing doorways, and it stays quiet in a way the cliff villages do not. Give it a morning, then spend the afternoon on the coast.
2. Sunset in Oia
Do it once, and do it on foot. Oia is the most photographed place in Greece, which is not a thing you need to be told twice, and by late afternoon the lanes facing the water are full of people waiting. Arrive with time to walk away from the main street, find a step on the caldera side, and sit down.
The twenty minutes after the sun goes are better than the ten before it. The crowd starts leaving, the white walls go pink, and the village belongs to whoever stays. Eat in Oia afterwards, once the tables have turned over.

3. Take a Catamaran Around the Caldera
The four-hour sunset cruise leaves from the marina at Vlychada and works along the deep blue water off the island, which is the angle you cannot get from the cliff above. It runs to Red Beach and White Beach for a swim, then past the Black Mountain, also called Indian Rock, and the Venetian Lighthouse.
Later it puts you in the hot springs at Palea Kameni. From there the boat crosses to Thirassia, the fishermen's island, where the view back runs to Manolas village, and anchors for dinner on board with wine and dessert before returning to Ammoudi Bay. Book it for the first clear day of the trip, because wind and weather can move the plan.
4. See the Minoan Town at Akrotiri
Akrotiri is a Minoan city buried by the eruption and preserved under layers of volcanic rock, which is why it survived virtually intact. It is the Pompeii of the Aegean, and the comparison holds well enough: what you walk through is a town plan rather than a field of broken columns.
I would give it two hours. A licensed archaeologist guide earns the fee here, because the plan says less than the person standing in it does. Go in the morning, when the site is cooler and the groups have not arrived.
5. Swim at Red Beach and White Beach
Red Beach does not need the name explained: the cliff and the shore are the same color, and it is the one people photograph. White Beach is paler, smaller and quieter, and the boat reaches it after Red Beach. Both are volcanic, and both are better from the water than from a picture.
Come with water and something to sit on, because there is nothing to buy once you are down there, and pack out your trash. A swim at each is enough; neither needs a whole afternoon.

6. Taste Assyrtiko at a Winery
Assyrtiko is the local grape, and the wine it makes is what I bring home. A traditional winery will pour a short flight, from a young dry one to something with age on it, and a tasting is the quickest way to learn how far one grape can travel in a glass.
Book a tasting for the end of the day, when the room is quiet and the light is going. Buy a bottle for the room rather than shipping a case. Two wineries in one day is one too many; the second tastes like the first.
7. Drive Up Profitis Ilias
Profitis Ilias is the highest point on the island at 567 meters above sea level, and the road up ends at a monastery with a courtyard you can walk into and a small Greek Orthodox chapel. The view runs the length of Santorini, from the agricultural plains in the middle to the hilltop village of Oia.
Go up late in the afternoon, when the light comes in from the side and every terrace between you and the water shows up. An hour up there is plenty, and it is the fastest way to see how small the place actually is.
8. Spend an Afternoon at Perissa
Perissa is the black-sand beach on the island, and the sand really is black underfoot, which means it holds the heat. Walk it in shoes and swim in it barefoot, and keep going along the bay until the umbrellas thin out.
Come for lunch and stay for the swim, then leave before the afternoon gets heavy. Why this beach rather than the ones under the villages? Because you can lie down on it. This is the one that feels like a normal beach day rather than a viewpoint.
9. Walk the Volcano on Nea Kameni
Nea Kameni is the volcano in the middle of the caldera, the dark island the boat trips pass on the way to the springs. Standing off it with the cliffs on three sides, the shape of the caldera makes sense in a way it never does from the villages above.
Pair it with Palea Kameni next door, where the hot springs are, and take the swim even if the water looks strange. It is warm, it is the oddest swim of the trip, and you come out of it with the whole caldera in front of you.
10. Sleep in a Cave House
Some rooms on the caldera side are carved into the cliff itself, with rock walls, low curved ceilings and a terrace cut out of the slope. They were houses before they were hotels, which is why the layouts are odd and the doorways are small.
Book one for two nights rather than five. The novelty is real and the rate reflects it, so a cave room earns its money on the evening you watch the water from your own terrace instead of standing behind a wall of strangers.