We did similar trip last year but with P&O on the "Aurora". Would suggest the Cavtat and Dubrovnik trip Cavtat very picturesque and lovely visit for photography expected to see signs of the previous war but everything is repaired and no signs of the troubles. Dubrovnik was also excellent a walk around the walls of the city is great although this cost and extra charge but only a couple of pounds so it was well worth the cost. My wife and I also found an excellent bar, other end of town from the main gate turn right at the main square and church then through what looks like a small hole in the city wall. There was a small bar perched on the rocks outside the walls with brilliant views (We could have sat their all day).
Corfu is quite cheap and not too large - Therefore it would be better to get a Taxi to get you around (Make sure you agree a price first though). Have a look at the website http://www.kassiopi-experience.com.
Pireaus - Athens if quite good if you want to see the Acropolis. If they are doing a trip through the Corinth Canal that would also be a good choice.
Naples - Either of the tours you mention are good. However, it could possibly be better getting a Limo or Taxi to take you around (Again agree a price first) as Barry said. this way you could choose what you want to see. Keep an eye on the time though for returning to the ship.
Santorini - Never been there but was told by a friend that he enjoyed just walking around the island.
Cvitavecchia - It is easier and cheaper to get the Train to Rome and do your own thing , But again check the train times they have an habit of cancelling some !
Livorno - We only spent about 2 hours in Pisa it was nice to see as indeed was Florence, but unless you want to see more ove these then If you have the choice of a tour of Tuscany I can say that the country side and visits well worth it.
Villefranche - Is a nice town and unless you really want a tour, it is cheap and quick to get the train to Monaco which is quite an exciting place to visit
Barcelona - Has some interesting places to visit, which you can do by yourself, but as you say it is very cheap so what the heck.
My only advice is to remember that tours usually include entrance fees to various Palaces, Churches etc... etc... and also a meal if it is a full day tour. So it is still worth considering the tours.
What every you do enjoy your cruise and tours as I am sure you will.
Best Regards