Hi anya and djjazzy. Forgive me for not getting back to you sooner.
Anya, we did ship tours in most ports, including Rome. Still, we never felt rushed or overwhelmed. As for Rome, the city is so large that it is impossible to see a good amount of it in the time we have there, no matter what kind of tour you use. My advice is to hone in on a couple of areas you want to see most and focus on those. This is how the professional tours do it. If you are on your own, stop by the Shore Excursion desk and they will help you map out a route and will also let you know how ambitious it is. Again, just keep in mind that you won't be able to see most of the city in this short a time period.
djjazzy, on our cruise, the Port Authority ran a shuttle from the pier throughout the day. The price was 5 Euro per person for a day pass. I do not know the drop-off point as, once again we were on a ship tour, yet that info will be available on the ship. In Palma de Mallorca, a similar service was 10 US dollars, and dropped us off across the road from the Almudaina Palace and Cathedral La Seu. We had a very pleasant walk in Palma, using a great map that was on the seats of the shuttle bus (but, bring your own just in case). I highly recommend a walk down the Passeig del Born... very pretty and lively.
Dave, the MDR was stunning. It had a similar entrance to the Windward Dining Room on SS Norway... the stair tower led directly to the entrance, then another flight of stairs to descend into the MDR. The decor was very ocean-liner-like... losts of dark brown columns. Key difference was that there were windows on parts of two sides and one large one aft. Decor paid tribute to Matson Line menu covers, supposedly, highlighting the history of Hawai'i. (As you know, N. Jade was previously Pride of Hawai'i.) And, the food was fabulous. We dined there three of the seven nights and once for lunch.
I have to rush off to work now, but will be back later this afternoon with information about what we did in the other ports. In brief, they were all ship tours -- Nice, Eze & Monaco (Monte Carlo), Splendor of Florence, Roman Highlights, and Flavors of Sorrento & Pompeii (Naples). Enjoyed them all.