3 Days in Santorini

Don’t stay all the way over in Kamari. Santorini is not known for it’s beaches.
Perhaps cut a night from your stay; we found four nights too long.
Visit Akrotiri, and Amoudi Harbor. Look at the view. Then go to another , more Greek feeling, less over run island.

Even if the recommended hotels are sold out that does not mean you can't stay in Firstephani. Just go to a booking site like booking dot com and enter Santorini and your dates and it will give you lots of hotel options. Firostephani is a good choice. It has all the same wonderful Caldera views but its just far enough from Fira that the cruise ship crowds don't come up that far as they are concentrated in Fira and Oia.
Its actually a great walk along the caldera edge path so you can be in Fira after sun set for dinner. The crowds will be thinning by then.

You haven't told us what your maximum nightly room budget would be. Without that we can't realistically offer any recommendations.

Accommodation considerations: two adults, 4 nights, at the end of April/2020, caldera view, walking distance of FIRA (we walk/hike a lot), no need for fancy or pool. We thought we would pay more for the once-in-a-lifetime experience, rather than being further inland.
We found one such place in FIRA at 600 USD (800 Cdn) for 4 nights, which would probably be our price limit.

Standbr's suggestion of checking Booking.com is promising with a couple in the 500 USD (600-700 Cdn) range in Fira and one for less in Firostephani.
What about south of Fira? There seem to be nice AirBnB's in that area.
Thank you.

It would help if you said the hotel names not just "one such" or "a couple" unless you don't really want advice.

I would recommend Santorini Secret Suites in Oia. It is an outstanding hotel with caldera views and a quiet small hotel. They bring breakfast to your terrace in the morning. It is a wonderful oasis in Oia. Booking.com still has a pure suite available the last week of April for $489.00 for example and tripadvisor has other rooms with this hotel also. It has a lovely infinity pool and a private hot tub on your terrace. We really enjoyed Oia and took walks on the promenade in the morning and had dinner at restaurants with sunset views in the evening. We took the bus from Oia towards Fira and asked the bus driver to drop us off in Imerovigli and then hiked downhill to Firostefani and Fira and took the bus back. It was also easy to take the bus to Akrotiri to see the archaeological ruins there. In the afternoon we enjoyed the pool and hot tub in May. Best wishes for a great trip!

Organizer, I think that OP mentioned $600USD for 4 nights which means $150 per night... if your quote of $489 is for 4 night, that is terrific -- but if for one night, way out of his budget. It would help if everybody is specific about days & prices.

We stayed at Nikos Villas, just outside Oia. It was close enough to walk to town and far enough away from the cruise-ship tourists.https://www.nikos-villas.com/
I highly recommend using Kostas as a tour guide
https://santorini-private-guide.com
There's not much to fill 3 days. Kostas will take you around the whole island, including Akrotiri and the monastery. Plus spend one day exploring Oia and Amoudi Bay. Of course, the sunsets are amazing.
Have fun!

We have booked this hotel for 2 nights in May 2020
Sofia Hotel Santorini
Firostefani 84700,
Tel:. +30 22860 22802
[email protected] R
Rm 105.The price is 110,50 Euro inclusive all the taxes. If you pay in cash we can do 99,50 Euro per night.

It looks very nice and the price is very reasonable, as you can see.
Good luck.