Thank you all for your suggestions! This was very helpful and I will look at all the places suggested. I can tell that Naxos is a much loved destination! I might shift a night from Mykonos to Naxos, but I'd appreciate the recommendations in Mykonos all the same. I'd like to hear about Santorini, too, if anyone knows of a well-situated hotel? Our group of 7 may be reduced to 6 now, so we would need 3 rooms. Since we don't plan to spend much time in them, they only need to be "good enough". We'd rather spend our money on a phenomenal meal than an extravagant hotel. That said, if we need to spend a little more for an ideal location, we can do that. (The exchange rate is favorable right now.)
To Charlene: I know that Ikaria will require a short flight. I really want to go, but depending on scheduling, it may not be feasible. What other islands would you recommend?
To Jolui: We booked our flights through to Mykonos. We'd take the ferry to Naxos, then onto Amorgos (for a retreat we are attending), then to Santorini. There is the possibility of a flight to Ikaria, and then back to Athens for a few days before flying home.
The reason I hesitate to post in this forum is because people often question how ambitious my trips are. Rest assured, I am a seasoned European traveler, and I really do "travel" when I'm on "vacation". In fact, we visited 6 countries on our 2-week honeymoon! I know my itinerary is doable because I've done my research, but thank you for your concern.
To Janet: I limited the details on purpose, as they truly aren't relevant to my question. A hotel in each locale is either recommended or it isn't, regardless of when I am visiting. The length of my trip is of no consequence to whether you are able to recommend accommodations or not. I did specify that our group is comprised of 2 couples (4 people, 2 beds) and 3 singles (3 people, 3 beds), and I said I was looking to book 3 or more rooms (which might rule out a bed and breakfast, for example). If you know of a villa you'd recommend, please share it and then I can decide if I like the location. If you've stayed there and you were satisfied enough to recommend it, what reason would I have to not consider it as well? And if I don't take your suggestion, you are no worse off for having offered it. I am sorry you are spending more time than necessary trying to figure out what I am up to!