Hi Terry, I am going to try and help but keep in mind I do have my personal biases and prefer to travel independent of tours. Most cruise ships will make a morning stop at Delos, let the passengers off the ship who are taking the tour of the ruins,, and than proceed to Mykonos (about an hour away by boat). Some ships wait off Delos,,, and others will have the tours get to Mykonos by smaller local boats where you can later meet the boat. Yes, the ruins (and the so-so museum at the ruins) are normally closed on Mondays. However, sometimes the cruise lines arrange for the ruins to be open for their tours on Mondays.... You are going to have to check your cruise line tour schedule for this info. There is really nothing on Delos other than the ruins...in fact, nobody lives on Delos. The workers at the ruins all commute by boat from Mykonos. Although there is boat service between Mykonos and Delos, its very limited unless you are on a tour. Personally, I think that the ruins on Delos are very disappointing when compared to other ruins in places like Athens, Pompeii, Ephesus, and Hurculanium. Mykonos is an easy island to do on your own...since you will dock near (or tender into) the town. Mykonos town has nice cafes on the water, excellent shops, and everyone is very friendly. The island is also famous for its beaches, but in mid-November it might not be great beach weather (not sure about this). In Santorini, if you want to spend your time in Fira (wonderful place) and Oia (smaller but precious) you can do this on your own by simply using the cheap (about 1 Euro) public bus that runs between the towns. If you are thinking about exploring the remainder of the island you are going to either need to rent a car (not a problem), book a tour, or hire a car/driver. We have been to these island many times and Santorini is very special. Many are content to spend their first visit just walking around Fira, and perhaps Oia, and enjoying a nice lunch at one of the many cafes that offer amazing views. I sometimes think that many tourists spend too much time running running running, and do not allow themselves time to sit at an outdoor cafe, sip some wine, have some food, etc. But this is a personal opinion and there are many who just like to run run run
By the way,, there is lots of fun shopping on both of these islands. Be careful in Mykonos, because they have some great (very expensive) jewelry shops. I have to put "blinders" on my wife when we walk in Mykonos.