Palma de Mallorca

Most of the beaches around Palma are not very charming. It's mostly holiday resorts for Northern Europeans with big, ugly hotels, where you can find little colonies where the british eat british food in british restaurants, germans eat german food in german restaurants, Scandinavians eating scandinavian food on scandinavians restaurans etc. not very charming.
One good option for a day trip is the old steam train to Sóller on the north coast. http://trendesoller.com/en/home/ It's a scenic trip trough fields, valleys and trough tunnels in the mountains until the train descends trough a series of switchbacks down the the Sóller . Sóller is quite charming in itself, but for a beach trip you can take the equally charming tram down to Port de Sóller, where there is a pleasant beach. It's still full of tourists, but the town and area has retained most of it's charm.

I don't know about the beaches but the cathedral is huge and truly amazing and worth a visit, also Mallorca is known for their man made pearls and it is interesting to visit where they make them and see how it's done. Lastly, there is a round fort that sits above the main town overlooking everything and if your into interesting architecture, it is awesome.

The train ride to Soller is certainly worth doing, as is the following tram journey down to Puerto de Soller, But neither is a steam train. They use vintage electric trains, which are charming but without the soot and noise. Both Soller and Puerto de Soller are attractive and popular destinations, but they do get lots of visitors, so possibly not the places to go if you are looking for solitude and tranquility.

Bob, your absolutely right, it's not a steam train. In my head that was the word that popped up when I thought of vintage trains, but of course it is not the same.
The round fort above the city that Donald mentions is Castell de Bellver. https://castelldebellver.palma.cat/portal/PALMA/castelldebellver/castelldebellver_principal1.jsp?codResi=1&language=en
It is indeed very interesting from an architectural perspective since it's one of the only medieval castles with a completely round shape. it also houses the Palma city museum.

The best beaches are not to be found around Palma and with only a day to spend on the island it's not worth spending time to get to them as you would need to rent a car and devote at least half a day. Playa de Palma isn't bad by any stretch, it's quite cosmopolitan and whilst nowhere near as scenic and unspoilt as Es Trenc or Cala Mondragó it's certainly not like the British enclave of Magaluf or the German equivalent in S'Arenal.

Palma is a fantastic city, one of Spain's best in my opinion. You can easily fill your day there. Here's a brief guide for 36 hours in Palma so you can pare it down to what suits you.

https://www.telegraph.co.uk/travel/destinations/europe/spain/majorca/articles/36-hours-in-palma/

There's a recommendation for restaurant Marc Fosh. We ate there in December as I've been meaning to try it out for some time. I was a bit disappointed, it's a lovely looking restaurant with fantastic staff and service but the food was lacking and didn't justify the hype, excellent Mallorcan wine though. I probably wouldn't return but there are plenty of restaurants to choose from.

You will need the cruise's shuttle bus (?) to get downtown from the boat. I agree that this is a much more attractive town than on most of the Spanish islands. The cathedral is lovely and can be visited without the ship's tour. There are plenty of places to have lunch in the old town, which is a nice stroll. We didn't investigate beaches, so I can't help on that.