Just got back from the June 6-16 cruise and I'll try to post a trip report later, but thought I'd give input here to start...
First of all, let me say the trip was wonderful and exceeded my expectations!

We traveled with two small children and did most excursions on our own. With a 2 and 4 year old, we took the approach "less is more" when it came to seeing things. When excursions got too long, it wasn't too much fun for anyone.
Here are some highlights:
Palermo: We did the Mondello Beach tour with Disney in the morning and really enjoyed it. I had tried to get information on taking our own transportation and never did find it. In addition to getting ground transportation, you get access to private area of the beach with chairs, plus a free gelato. Glad I did the tour.
Naples: We took the hydrofoil over to Capri, which was super easy. Just walked a few hundred yards from ship to hydrofoil and purchased tickets at a ticket booth. I think it was 15 euros each way for adults and small kids were free. Capri was beautiful and we took the funicular up the hill (which was very inexpensive).
Olbia: Again, here we did a Disney excursion, as I couldn't find much info on self excursions. Took the Train to Galluria. It was a beautiful bus ride and train ride and we even made a brief stop on Costa Smeralda on way home. Probably a bit too much bus and training for our active 2 year old. I think spending the day on the beach would have worked better for us.
La Spezia: Loved this port!! We took a 10 euro taxi ride from port to train station and then bought round trip tickets to Monderosso in Cinque Terre for about 10 euros (for both adults round trip) at train station. It was an easy trip. We made a stop at just one of the Cinque Terre towns, but I'd recommend doing a bit of research and stopping at a couple (or more). BEAUTIFUL, friendly people, great food. Definitely easier/less expensive than going to Pisa or Florence and very beautiful.
Marseilles: We took the free shuttle into Old Port and just walked around. Honestly, it was a bit trafficky and noisy for us at Old Port. Probably our least favorite stop. There were lots of nice restaurants there, but I'd do a little more research next time and figure out how to get to a more relaxing and beautiful spot next time. Shopping and restaurants with two little ones isn't too much fun. Though we did find a merry go round right there in the center of Old Port which they enjoyed.
Villefranche: Wonderful port! Easy tender into town and a beautiful beach and lovely shops and restaurants right there! Train station an easy ten minute walk. We took a short train ride to Monte Carlo and walked around and then returned back to Villefranche where we spent a couple hours on the beach and then had crepes at one of the restaurants in Villefranche. Train also went to Nice and Cannes, but we just went to Monte Carlo.
Citavecchia: I had purchased train tickets online for us to do a self tour to Rome. But we were tired this day and decided to just stay on the ship, as I've been to Rome before, my husband needed some rest and the kids wanted to stay on the ship. Ended up being a wonderfully relaxing day. And I got a full refund online for the train tickets.
Barcelona: We got in on an overnight train from Paris the morning of June 16 and ended up just going to the terminal at 9am. I had intended to get out to Barcelona to see some sights that day, but didn't make it.
If you have any questions, let me know.