I'm the family cruise editor for CruiseMates.com. I think bringing teens to Europe is a great learning experience for them -- they'll be amazed at the differences in cultures, languages, food, architecture, etc. There are a number of ports on your itinerary that can be explored independently by you and your youngsters without having to purchase expensive shore excursions. They include: Venice, Athens, Barcelona and Istanbul. However, with Athens, you should purchase the transfer that the cruise line sells from the port of Piraeus into the heart of Athens. Then there's plenty to do on your own: Acropolis, cable car to the top of Mt. Litabekus, changing of the guard at the palace. In Venice, there's gondola rides, lounging at an outdoor cafe in St. Mark's square, and visiting the Murano glass factory. Barcelona features the Picasso Museum, the Sagrada Familia cathedral (the unfinished Gaudi cathedral), Las Ramblas boulevard, etc.
You may want to purchase shore excursions in Florence and Monte Carlo. Florence is over one hour away from the port of Livorno and museums, etc. get really crowded. You'd be better off with a group tour. In Monte Carlo, most ships dock in Villefranche which is a drive away from Monte Carlo, Cannes, Eze, etc. Again, a shore excursion is your best bet. Eze is a great little medieval village with winding paths that your teens would enjoy, stocked with boutiques and restaurants.
There's a book I highly recommend: "Cruise Vacations with your Children" published by Prima Publishing and written by Candyce Stapen. There's a whole section on cruising to Europe with youngsters and all the ports you mentioned are in there. Each port suggests things to see and do according to the youngsters' ages; naturally there are suggestions for teens. It's worth to do your homework before hand. Europeans are used to dealing with Americans and it gets way too expensive to buy group shore excursions for your whole family in each port. A better idea is to explore some ports independently and others via group tours.
Have a fabulous trip!
Luisa Frey Gaynor