Doing a Greek Isles cruise in June with our teenagers. I think we will see enough ruins in Athens and Ephesus so wanted to make Mykonos and Rhodes just about enjoying the outdoors. Should we rent a car and drive around? Take taxi to a beach or two? Or are there some not to be missed sights there?
We are also docking in Santorini but we were there on our honeymoon so familiar with things to see there. Thanks

Advice depends a lot on specifics, for example how long you have on shore, when you'll be visiting, how large is the cruise ship etc. Personaly I find Old Rhodes Town absolutely gorgeous and a pitty not to explore but it is true that it is far too crowded for my liking on high season when tens of cruise ships dock. I believe the second popular place that cruise ship passengers go is Lindos. So you may hire a car and head elsewhere, maybe stopping on said places towards the end of your day when crowds migth have ease a bit (hopefully). You may want to google Prasonisi beach on Rhodes and see if it appeals and drive there to spend a few hours, stopping on Lindos and/or 7 springs area on your return journey.
I now you said you are not into ruins, but it would be a pitty to miss Lindos Acropolis and the amazing view and having the car I would benefit to stop by Rhodes Acropolis on Monte Smith above Rhodes Town. I find Rhodes Archeological Museum one of the most interesting archeological museums I have ever visited in Greece, but I guess it might not appeal to you. In case your teenagers are into this kind of thing, there is a small aquarium on Rhodes Town too.
Mykonos is mostly about three things a)Its scenic town b) Its sandy beaches 3)The easy side trip to Delos.
If you are not interested on ruins, forget about c) although delos is one of the most importnat archeological sites in Greece.
About a) I am sure you will visit Mykonos Town at some point of your day, it is a pitty to miss it although it will definately be busy no matter when you go. Re the b) read up a bit and see which beach appeals. I would hire a car and chose a far away spot which is not served by public transport and have a beach day.

Well, that is a difficult decision. Both Mykonos and Rhodes have some unique sights, but beautiful beaches too. After being stuck aboard ship, maybe some beach time away from other passengers would be a welcome change. On the other hand there are beaches everywhere, maybe even some brilliant ones near where you live.

Have you asked the teens what they would like to do? No one knows your teens better than you, but it seems to me they may enjoy the cruise more if they have the deciding vote in one or two port calls.

I managed to drive around the entire island with a rental car, visit the old town and the Castle and take a break to see Lindos and swim, when i did a cruise to the Aegean Islands.
We arrived at 8 am and left at 6 pm which gave us plenty of time.

Too many ruins? Maybe not with the gorgeous deep blue water for the background. Second Lindos.

I appreciate everyone's advice. We are going at end of June (high season) but on a 140 people ship so hopefully maybe not too many other big ships there.
We are big Caribbean lovers and have been to Anguilla and Turks and have seen our share of beautiful beaches so I think I will do more sightseeing as everyone suggests.