We didn't do any organised tours in the Med because they were so expensive and also because we aren't keen on tours & like to do our own thing. If you do choose to do them, I'd be inclined to book in advance because the popular ones get booked up quickly. Independent travel in Med ports is actually really easy to do & shouldn't be too daunting. We managed with only a couple of words of Italian & my very rusty French.
I found great advice on the cruisecritic.com forum, and was able to plan all our trips from tips I got there. You'll find maps, port information, travel info & invaluable tips from seasoned travellers.
Barcelona's hop on hop off bus is great, but it takes a long time to get all the way around the route. We did this then had a mad rush to get back to the ship in time! If I did it again, I'd walk or take the metro to get around. Our ship docked very close to the city as far as I can remember.
We got a taxi from Civitavecchia port to the station, then took the train into Rome. From there we walked around the major sights. It was very manageable. We had a wonderful day.
I've not been to Corsica, but if it's like Sardinia and you need to go ashore by tender, be aware that there will be huge queues for the tenders first thing in the morning, and priority is given to people on the organised tours. We waited a couple of hours to avoid the queues. There were also queues to catch the tenders back to the ship. I think we waited over an hour.
We were travelling with 3 teens & we had a great time, loved every minute of it.
If I think of anything else, I'll come back later.