Greece & ?

Time of year? Total number of days you plan to spend in Europe?

The Wikipedia entry for Santorini International Airport (https://en.wikipedia.org/wiki/SantoriniInternationalAirport) lists cities with direct air connections. Unfortunately, there are many (thus not really reducing your options much) and--aside from Athens--all of them are listed as "Seasonal", which can mean different time periods for different flights. I'd guess, also, that some of the flights do not operate daily. For precise information, you'll need to go to a website like skyscanner.com to check schedules and fares. You should book directly with the operating airline when the time comes. It's very likely to be cheaper to buy your transatlantic flights separately from the intra-European hops.

Istanbul is a fabulous destination. It's a large city and worth a full week (or more) if you can spare that much time. I see that Aegean has flights between Istanbul and Santorini, which I believe you have already discovered.

In quickly scanning the list of destinations provided by Wikipedia, the only direct Greek-island connection I found was Aegean's flight(s) to Rhodes. Flying to other islands with airports would probably mean connecting in Athens or a more-distant city. Aegean and Sky Express have regular flights to Athens. RyanAir and Volotea operate Santorini-Athens flights seasonally. If you opt for connecting flights, be sure you know what you're signing up for. I suspect (but am not sure) some budget airlines may not offer true connections, meaning that if your first flight is late and you miss the connection, you might have to buy a new ticket to complete the journey.

There are of course ferries connecting Santorini to other islands, probably most conveniently to other Cycladic islands. Personally, I wouldn't choose Mykonos or Ios, both of which are reported to be really swamped these days. I liked Naxos, but I know it is a lot busier now than it was not long ago. The Direct Ferries website (third-party source of ferry tickets) lists these possible destinations from Santorini: Milos, Amorgos (Katapola), Serifos, Tinos, Syros, Rhodes, Chalki, Sifnos, Crete (Heraklion, Rethymnon, Agios Nikolaos and Sitia), Kimolos, Naxos, Paros, Ios, Koufonissi, Folegandros, Anafi, Athens (Piraeus, Rafina and Lavrio), Kea, Mykonos, Kasos, Sikinos, Thirasia, Karpathos (Pigadia/Karpathos and Diafani) and Kythnos.

My choice of a second island would be influenced by how many days I could spend there. Crete is wonderful, but it is large. I wouldn't choose it for a short stay of only 2 or 3 nights.

Istanbul would be a great choice.

But if you would like other ideas consider working backwards from Santori or the other island you choose checking their airport what flights from what European cities into there. There may be more or less depending on the season.

Enjoy the planning!

Istanbul is always a good choice. Wonderful city and Turkish Airlines has great flight paths from so many American cities.

You don't specify the date you will be traveling (for how many days?).

Many flights to/from Santorini are seasonal and served mainly by low-cost airlines from many European cities (the main low-cost airlines are Transavia, Ryanair, Volotea, and Easy Jet), as well as by the two Greek airlines Aegean and Sky Express.

Some European airlines, including Aegean, Greece's national airline, have not yet released their full flight schedules for the 2026 season. This usually happens around October/November.

There are no direct flights from Santorini to any other Cyclades island.

Regarding ferries, ferry companies publish their schedules approximately 2 to 4 months in advance, depending on the company.
Ferry frequency varies depending on the month and the route. Depending on these factors, it ranges from 1 ferry per week to several ferries per day.

Hence the importance of knowing your dates.

Thanks everyone... I forgot to put dates... early summer probably the end of May. In looking I also think Istanbul might be the best option. I have been there before, but am doing all the planning for my daughter's family. The only 'must do' is Santorini. My 16 year old granddaughter has chosen this place, but I would like to recommend another location in Greece as well.

I have been to Nafplio and Athens and they do not want to go to Athens unless they need to for a flight.
I loved Nafplio, however I think they are more looking for another island.

I will check out a few more and come back with other questions.

I forgot to put dates... early summer probably the end of May.

June 21st is the first day of summer. So is the trip in May or late June?

Without knowing how many nights you will spend on your trip, and how many of those are in Greece, it is
hard to provide ideas of where to go.