We stayed here for 4 days after our cruise. Barcelona is an amazing city! Lots of stuff to see, lots of things to do, and it feels like it's a city that never sleeps. Depending on the amount of time you have here, you'll need to schedule your visit accordingly but here are the main attractions:
1. Sagrada Familia - this is a must see, especially inside! Make your reservation online!
2. Casa Batlo
3. Casa Pedrero
4. Visit Parc Guell - very beautiful park with some works by Gaudi. Definitely worth it!
5. Walk along the touristy Las Ramblas
6. Take the cable car up to Montjuic hill and fort up there
7. Rent a car and go for a day trip to Montserrat (45 minute North of Barcelona). This is a must see if you have at least 4 days in the city.
One of my favorite ports of call. Really picturesque small town situated on a mountain with narrow streets leading to steep stairs everywhere. We went on the self-guided tour of the city walls and it was beautiful. You can buy the tickets at the local tourist office just as you enter the city through the main gate to the right of the large fountain. The second half of our day we spent on their local "Copacabana beach" 15 minute taxi ride from the city and 10 minutes from the cruise ship. It was one of the best beach days on the whole cruise! Water was warm and clear, and beach, although not sandy, was very picturesque. Highly recommend!
Monaco is beautiful. There is quite a lot of contrast between the poor Italian cities and this gem of a kingdom. The city is situated on a very steep mountain and so a lot of the walking is up and down steep windy sidewalks. Thankfully a lot of the city has public elevators that will vastly ease the effort required to get around. There are many beautiful sites within the city and everything is walking distance. You can also take the local bus or maybe even the hop-on/hop-off if you get tired of walking. Good sites to visit are: Monte Carlo Casino, Exotic Gardens, Prince's Palace (and the change of the guard at 11:55AM daily).
We met with friends here and took a ride down to Pompeii. The archaeological area is huge so you'll need at the very least 3 hours to briefly see everything. Quite interesting and worth the drive. We then headed out to Sorrento but did not have much time to actually stay here or walk around. Given the amount of time given at the port of call, it'd be pretty difficult to see both Sorrento/Amalfi Coast and Pompeii although definitely doable with good prior organization. The scenery around this part of Italy is breathtaking!
We had only 5 hours here. It was not great. Getting a cab here is next to impossible and bus schedule is horrible. Unless you have a well-planned excursion don't even bother. We ended up walking along the shore to the Cathedral (Le Seu) which was pretty beautiful and worth a look inside. The shoreline is actually pretty nice and there are some nice sights along the way but nothing too spectacular. Another option is to schedule an excursion with the cruise-line to go on the train ride to Soller. Sounds like a good idea maybe.
We already stayed in Rome for 3 days prior so we did not take the Rome excursion. But of course if you've never been, Rome is a definite must see. Although we heard from many people that the cruise excursion was a waste of time and money. It is very difficult to see Rome in the time that you are given. So in reality, this port of call is somewhat useless. We ended up going to the little town of Tarquinia but unfortunately for us it was a Monday and everything was closed. It is still a beautiful little medieval town and worth the trip. Note that if you go by train to the Tarquinia train station, it's about an hour walk to the city and there are no cabs in sight but there is a local bus that goes straight to the town right from the train station and follows a pretty frequent schedule so that would probably be your best bet.
Note: in the summer it's extremely hot and worst of all - humid. Probably the worst climate out of all our ports of call. Make sure you dress up very lightly. Here it's just all walking around. Make sure you visit St. Marks square and the Basilica (good idea to make reservation online as the line ups to get in are out of control!). Also take a Vaporetto (water taxi) down the main canal - this is an excellent way to see the whole city and admire the beauty all around you. If you are into classical music there is also excellent orchestra playing great works of Vivaldi etc: http://www.interpretiveneziani.com/en/. Otherwise just walk around the narrow streets, sit on a terrace have a meal by the water, and if you're really feeling up to it, take a Gondola ride (although many people online say it's not really worth the money).