Just for fun I looked at the Aegean Airline website. They have flights from Rome to Santorini with a couple of hours layover in Athens. Aegean often have very low fares on sale. You will likely start to see them coming up for next summer in the next couple of months. Sign up for their web site and get notification when the sales start. If you are quick you can get one.
There is regular ferry service from Naxos or Paros to Santorini and you may be worthwhile to backtrack back to Santorini to get a great price by doing a return flight to Rome.
You do know that Santorini beaches are volcanic pumice pebble not sand. They get very hot. Santorini is about the view while Naxos/Paros both have good beaches.

Thanks for the info, stanbr; I'll sign up for that website!

Marking for later use, thanks.

bookmarking