I am not a seasoned traveler to these spots (only cruised them once)
but when we were planning our trip, I found it very helpful to Google the individual cities. Many have their own websites now. Here's one example:
Livorno Now | About Livorno in Tuscany Italy
That was much easier and more concise than wading through the 'guide books'.
It is hard to recommend things to see and do to another, for what I might think is a must may be as boring as cold toast to someone else…. and not all have the same physical stamina that is often needed to see and do.
Time is an element as well- many of the wonderful things to see are not that close together…. or that close to the harbor- so often the 'cruise tours' are the better, safer bet.
You'll be driven in a brand new, air conditioned bus and will be assured of getting back to the ship on time. Once there, you are often 'freed' to meander on your own- unless it is a guided tour with a lecture, you are not kept in tight formation.
Unless you are very fluent in other languages, it can be difficult to head out on your own. Some areas are safer than others to wander through, as in any city.
Often, street signs are very old cornerstones of buildings- even with a map, you may not always be able to identify the street you are walking on, or headed to. You may easily miss something cool, not knowing it was only a block away.
We spent time going to places, only to find them 'under renovation' and closed to the public that day. (not so uncommon, and very disappointing) In those instances, we'd have been better off choosing a tour.
We did both guided tours and independent exploration. We saw more on the guided tours, generally- and were less exhausted.
If you have a day in Barcelona, do consider seeing some Gaudi architecture. (it's NOT boring!)
You can easily to THAT independently- there is a bus that will pick up and drop off at appointed stations. The bus comes by once an hour. Very pleasant way to go - I think the bus pass was about $14 for a 24 hour period and the stations were marked on a map that came with the pass.
Have a great time- and tell us what you enjoyed when you return!