Embarked at lunchtime, so having the afternoon to explore Palma on day one was a bonus. Possible to walk into town - perhaps 30 mins, alongside the marina - we took a taxi (10 euros each way) and there are public buses between the port and the town. The cathedral is spectacular, but open only in the morning. We enjoyed wandering around it, then into the narrow streets and stopping for coffee in a cafe in a shady square. Felt relaxed and safe.
Sleepy little fishing village, accessed by ship tender. We took the train to Monaco (running twice every hour, about twenty minutes / 5 stops, reasonably cheap and scenic, don't forget to get your ticket validated in the yellow machines on the platform, both ways). Monaco was worth the effort, we took the hop on hop off tour bus ('Le Grande Tour', a little expensive at 24 euros, but good to see everything in a limited time, find it by walking down from station to the harbour). Don't miss the casino - we paid 10 euros to go in and nose around whilst there was no gambling going on, recommended. If it's open (after 2pm) you can go in as a gambler - if suitably attired. Great lunch at Pizza Du Stad (11 Avenue des Castelans, 98000 Monaco) not much to look at but good value, in a shady side street near Port de Cap D'ail, between stops 9 & 10 of the tour bus. Returning to Villefranch we enjoyed a stroll through the old streets and a coffee at one of the many restaurants along the water's edge. Small and relaxed place, not much to do. There's also a small beach and a tourist train.
Lucca is a fantastic little town, overlooked by tourists. We chose the Thomson trip - £32 each - because a taxi from Livorno dock to the train station was 20 euros each way, then it's two trains to Lucca, changing at Pisa. Note: the shuttle bus (5 euros return to town) goes nowhere near the train station in Livorno. 40 mins each way on the coach (with informative commentary) and an enjoyable walking tour, followed by an hour free time. Just enough time to enjoy a coffee in the atmospheric former roman oval amphitheatre (amazing) then walk along the town walls that make Lucca unique.
Tender from ship to Rapallo. A lovely non-tourisity place, we strolled along the front, enjoyed (real) cappuccino in a back street then caught a local bus to neighbouring Santa Margartia - a lovely horseshoe bay to stroll and enjoy lunch. Portofino is another bus ride from there (8km from Rapallo in total, I believe). Buses depart from near the train station in Rapello, tickets are 1.5 euros, from a machine or the newsagent stand and should be validated when you get on the bus, in the yellow machine (they can be used for all journeys completed within 100 mins).
Tuolon (not Nice, which isn't on the dropdown menu!). Enjoyed strolling along the marina in Toulon, into town where an buzzing market was in full swing. Had coffee with the locals in a quiet square. Then took the tourist train to the beach, which is worth a visit (the train is a bit naff though, consider walking or take a taxi to the beach instead). Not a great deal to do or see in Toulon, but an enjoyable place to explore (not touristy, rather run down on places, but quite charming). Huge bay area, which provides for a scenic 'sail away' (check out all the navy vessels).
Our ship moored next to World Trade Centre, right in the heart of things. Caught the Metro to Guadi's Sagradia Familia, a good way to travel (clean, easy and air conditioned - cheap too, around 2 euros). Tip: book a time slot online online for Guadi's famous church, thereby skipping the queue (either beforehand, or when you get there, by going into McDonalds opposite the ticket office for the free WiFi, then just show confirmation on your smartphone to gain entry). Parc Guel right at the top of the city is worth a visit (no access by Metro, 6 euros by taxi from the Sagradia Familia, or take a bus). Park entry is now 8 euros (for the main part of it). If it's busy, you'll get a time slot - go and look around Guadi's home / museum (5 euros) or grab a snack at the bar in the centre of the park - with fantastic views over the city - to pass the time. We ended our day wandering through the narrow streets of the Bari Gothic, enjoying the relative peace and lack of traffic, a fabulous place to stop for refreshment. Then down La Ramblas, a famous pedestrianised street full of street performers and artists' stalls, back to the ship.