I did some island hopping in Greece and Naxos was my first and also my favorite island.
Generally about island hopping in Greece:
I booked the ferries before (because I thought the prices are cheaper this way) my arrival which actually was not necessary. Some of my booked ferries didn't go in the end and I had to change and get a new ticket anyway.
On the islands you can either rent a scooter or car or take the tourist busses to the places you want to visit. Exploring it on your own you are surely more flexible. But I was a little scared alone because of the small streets.
So in Naxos you have the Temple of Apollo (Portara) directly at the beach. It is definitely worth a visit.
Another highlight for me was to see the inside of the island. I took a bus and having arrived there I was surprised of the beautiful landscape. Actually I went there to go to the Temple of Demeter which I didn't find in the end. Obviously it is harder to find walking there (maybe by car it's easier). But it was still worth it.
My second island was Ios. I stayed on this island for two nights.
The beaches are really nice and the sunset is beautiful. I also recommend to visit the port to see the sunset there.
In the center of Ios there is a very cute church. You can take a walk from the small village center to the port which goes downhill. The church is called Church Panagia Gremiotissa. There is also an old windmill around in this area which was quiet interesting. There are some small shops and it is nice to take a walk around.
At the beach you can enjoy a cold coffee (frappé) which are really tasty and good to relax from the warm temperature. I went to visit Greece at the end of the season. So it was quite calm and there were not many tourists (which I like). So if you plan to go there during the season, it might not be so calm.
I know that Santorini is a very touristy place and everyone is going there, but I think the sunset really IS amazing and that it is worth going there. So if you don't mind crowded and touristy places and you can enjoy the surrounding nevertheless, I would recommend visiting it.
Another beautiful thing about this island is its shape. The cliffs on the side of the island where you can watch the sunset are very steep and it just looks amazing.
In other parts of the island there are beaches where you can go swimming. I stayed in Perissa where are beaches for example. Close to Perissa there is also the Ancient Thera. You can walk up the hill there.
I also did a tour to black, white and red sand beaches which are only reachable by boat.
Right next to Santorini there is a small island (Tholos Naftilos) with its active volcano. You can go by a tourist boat there and you get a tour. There is one place where you can feel the heat of the volcano.
Q & A
What would you have changed?
Maybe I wouldn't book the ferry tickets in advance the next time.
Anything go wrong during the trip?
Just the ferries that were cancelled (that I booked in advance), but there was always another possibility and I didn't have to pay extra or on top
What tips would you give a friend?
good shoes to walk on the countryside
Buses are ok, renting your own scooter or car is better.