We will be going to a wedding in Santorini the end of May. So, flying into Athens, taking a flight immediately to Santorini for 2 1/2 days and wondering what island to go to from Santorini. We have 3 days to spend somewhere , then will go to Naxos for 3 days and then fly to Athens for 2 days-before flying back home.
Without any hesitation: Amorgos.
Santorini to Amorgos (1 hour 20 minutes with Seajets), then Amorgos to Naxos (3 hours 30 minutes with Express Skopitilis)
Agree with Jo-Lui.... of the 2 places iln Amorgos, I prefer Aegali for lovely small beach ... Amorgos is difficult to roam around in without a car, since local transit is sparse, but you can enjoy that beach AND walk up to 2 lovely villages on the high hills behind, & walk between the two, even have ealy supper on a taverna there before sunset -- as long as you make sure to catch the last bus downhill .... I remember we just managed it, a bit before 9 pm. Wherever you stay, check your hotelier about timetable.
Amorgos places - a whiile since I was there, but I believe this place is still a going concern, not fancy but friendly, just back from beach about 200 yards, surrounded by greenery, has a llittle cafe for breakfast, and is sociable in evening (it has a camping area close by, but not rowdy). http://www.askaspension.gr/
You might decide that you could use those three days in Naxos which will give you 6 days in Naxos. Honestly Naxos really needs a week to experience what it has to offer. Naxos is also a good companion island as a contrast from all the hype of Santorini.
Every island hop you make will eat up a half day just getting from one island to the second island. By choosing to just stay in Naxos you will have an extra half day to enjoy your trip.
This is why extending your Naxos trip is your best option.
https://www.flickr.com/photos/stanbr54/albums/72177720334044112/
Thank you for the recommendations and advice!