Which Greek Island?

What travel guides did you read to select Rhodes, Mykonos and Crete?

Santorini is in the Cyclades Islands, Rhodes is in the Dodecanese Islands.
Going directly from one to the other is practically not possible.
Much of the history and culture in Mykonos consists of nighttime parties with or without showbiz stars, but with foam cannons.
Crete is easily accessible by ferry from Santorini but this island requires at least 10 days to be partially visited, so don't plan to "explore" it.

Naxos, Ios or Amorgos could also be alternatives easily accessible from Santorini.

Of the three islands you give I’d choose Rhodes for its long history and your short time. Crete is an Island that requires a minimum of a week to just scratch the surface. Mykonos is party central though probably quiet in April. The island of Delos with its ruins a short small boat ride away but the sea can be notoriously rough because of the winds the area is noted for.

Weather in April is typically springlike with temps on the mainland around 20c in the daytime and half that at night. Rain is a possibility. It may be cooler on the Islands but will be warming up towards the end of April. The sea will be too cold for swimming but beach time should be possible. Nice time of year for tramping around sites and humidity should be low. So pack for all possibilities! You definitely will need a jacket or sweater for evenings.

Of the three islands you give I’d choose Rhodes for its long history
and your short time

If they are in Santorini, getting to Rhodes will take them around 20 hours by ferry and there are only 2 ferries per week in April.
Or they will have to return to Athens and take a flight to Rhodes

Agree with JoLui you need an island on a direct ferry route from Santorini. If it were me I would ferry to Naxos. It is still early season but Naxos will be active with early vacationers. Plan to stay at St George beach, It is part of Naxos town so you get a beach and the town just a 10 minute stroll away.
Naxos has a few antiquities along with mountain villages with good hiking opportunities.

We were in Crete first week of May. The weather was warm during the day but we needed sweaters or a light jacket for evening dining (which tends to be outside) Since you are going in April bring something warm for the evenings.
Here is why I suggest Naxos.
Naxos 2022. https://www.flickr.com/photos/stanbr54/albums/72177720299940917/
Naxos town 2022 https://www.flickr.com/photos/stanbr54/albums/72177720299959098
Hike around Chalki https://www.flickr.com/photos/stanbr54/albums/72157712247853233
Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689

Naxos !

Mykonos is expensive . And frankly just too “ Hollywood “ Gucci shops etc lol - you’ll see that in Santorini so why see them again , Naxos is lovely and more authentic as people live there year round . April is early season but I imagine while not swimming weather you may have some nice days for touring about and get some sun too .

Thank you everyone for the advice and knowledge! Any of these islands are either a 2-4 hour ferry ride or flight ( with change in Athens) to Santorini. So I’m not worried about transport between the islands. We have three full days with a travel day on either side for this trip. Mykonos, is the launching point to visit Delos, but I could pass on the ritzy party climate of the island. While we won’t have much time to explore the entirety of Crete— we would have time to visit the site of Knossos and make a few side trips around the area. The ferry to Santorini from Heraklion is only two hours long. I see all of these locations as logistically doable—rather which area is the most enriching historically? Following the advice above I would cut out Mykonos and narrow it down to Rhodes or Crete. Thanks for your insight!