There are first-class boats in the Aegean Sea that will take you to several other islands if you have the time to do that. They are very inexpensive and very easy to board from the Harbor. Just make sure you are there when the boat arrives to get on. I would recommend 40 minutes before departure. You will also need to get a reservation online. I use the following:
https://www.ferryhopper.com The best
https://www.directferries.com Also very good
https://www.ferries.gr/en/ A bit cheesy, but it shows some routes that the others do not.
Don’t worry about booking too soon, they rarely fill up. Also, there are fast ferries, but sometimes the slower ones are more enjoyable since you can sit on the top decks.
You can also take the ferry from Santorini to Athens, but keep in mind that it is a 7 hour trip, so a plane may be a better option here.
Some recommended ferry hops that also have flights back to Athens are below
Paros
Can’t say enough about this island, you definitely want to stay in Naousa which has a lively area to eat and drink in. If you have a car or ATV there are also tons of unique beaches all over this small island. As for Naousa, you do not need to stay on the water and I would recommend using Booking.com to find a place. We stayed at the Anemomylos Residence which was right across from an ATV rental place. Just a short walk to the harbor from there which is where all the restaurants and bars are.
You can see my pictures from our last trip there on Flickr
Mykonos
This is the island to hit for the best nightclubs of all the Greek Islands. They also have great beaches and restaurants. It is a bit expensive compared to other islands. Most of the action is in the Old Harbor on the West side of the island.
Naxos
A bit less touristy, but quite a bit to see here. The best places to stay are Plaka Beach or Naxos Town. There are also other resorts scattered in more desolate places on the island. We have not been here, so I can not make too many recommendations.