Choosing a Greek Island and with 3 teenage kids

Mykonos may be a bit "adult" for your kids, depending on the beach chose, but any of the others would be just fine. Paros is popular with many looking to stay out of the Mykonos-Santorini tourist crush and an easy ferry ride from Athens as is Andros or Syros. Kos and Rhodes as you said get good reviews as well, but certainly a much longer ferry, you may consider flying, but given you are open to options, simpler transportation may be a plus.

Thank you Paul. We are considering Naxos and taking a ferry there and then flying back to Athens. Wondering how the ferry ride through the islands would be.

Naxos is nice as well, and fits my rules for a ferry. I do not like ferries that are more than 3-4 hours, maybe at the longer side, but there should be a few stops on the way, and heading into a port and out is always interesting. Aside from that, ferries are sort of basic, and surprisingly, little open deck on many of them. Flying back is common, look at Aegean Air, Olympic Airlines also is competitive on domestic routes as well. Naxos is a bit of a larger island, more of a year round active island. I have been to the main port and have spent a couple nights, but really do not know much about other areas, other than I have heard they have nics beaches and several beach hotel areas scattered around the island.

There's nothing 'basic' about the Blue Star car ferries including the one making the run between Athens/Piraeus and Naxos. They're modern, have excellent facilities including sleeping cabins, aircraft-style lounge seating, cafes and snack bars and VIP seating areas. Deck space is fairly limited but you can get out and enjoy the sights as you enter a harbor.

It sounds as if you are leaning towards Naxos, which is a great island. In case you're still open to some other suggestions, I thought I would address some of the others you mentioned.

Paros is also very pretty, very similar to Naxos. Both have good beaches, and offer day trips to the sacred island of Delos, which is worthwhile if you have the time. Both are about 3-5 hours by ferry (depending on if it's a fast catamaran or slower ferry) from Athens, and less than an hour by air. I personally prefer using a ferry for short hops like this. But if you think you'd rather fly, I would recommend that you firm up your itinerary and check into tickets ASAP.

Both Aegean and Olympic airlines offer "tiered pricing" with a small group of lower priced tickets, and then progressively higher prices. If you are going this summer, it may already be too late for low prices in the Cyclades. I just priced June 19 one way from Naxos to Athens on Aegean, and it would be 400€ for the five of you.

On the other hand, I priced round trip from Athens to Kos on Aegean for the five of you, June 19-23, and it was just 373€. Kos is a beautiful island too, in the Dodecanese chain near Turkey, with some good beaches. But my favorite thing about Kos is that from here, you can easily visit the nearby tiny island of Nisyros. This island has an active (but not erupting volcano); you can hike into the crater, which has steaming fumaroles and soft, warm spots on the surface. We found it fascinating ... like walking on the moon. You can take a day trip from Kos and visit the volcano as part of a bus tour, but even better would be to ferry to the island early in the morning (or even the night before), rent a car, and get to the crater when it first opens. That's what we did (stayed overnight), and we had the crater all to ourselves. The island is easy to drive (there's just one road) and also has a pretty little yacht harbor. It also has a good museum which demonstrates how the island was created from volcanic eruptions, and a pretty little white, Cycladic-looking village nearby for lunch. We loved it.

I guess I can clarify basic, yes most larger, newer, ferries are nice, have a number of amenities, but often I find people equate ferries with a cruise ship, they are not, they are daily working vessels. So if the expectation is that you will spend the hours on an open deck cruising the islands, you maybe need to adjust. If you expect someplace somewhat comfortable sit, something to snack on, and transport from point A to B, then you are in the right frame of mind.

agree that naxos is a lovely island.
i don't know if i would want to go to mykonos with kids of the age you have.
i think a great island to consider is crete. something for everyone! there is tons of history, beaches, hiking, sporting activities, shopping. i enjoyed my time there and plan to return. i was a solo traveler but i really thought what a great place for a family.
easy, quick flight from athens. not sure how long the ferry ride is. i know it was approx a 6 hr ferry trip from crete to mykonos though.