Civitavecchia - travel to and from

Florence is lovely, worth a trip and once there easy to walk around with lots of cafe's markets etc and things too see.

Genoa - only been to transfer but very big port so probably need a shuttle into town

Marseille - again a big port, take the shuttle (there is an independent one far cheaper but a bit of a walk from the ship) and easy to walk around the harbour.

Barcelona - love it, you can walk from the ship but it will take around 30-45mins, a shuttle is provided, but once in town lots of walking for all the shops etc, just be careful about pick pockets around Las Ramblas area.

Mallorca - you can walk in or get the shuttle, easy and mostly flat, the Cathedral is worth a visit

Cartagena - easy walk into town (you berth quite close), nice castle on top of the hill, there is a lift up to it on the right - some Roman history also.

Gilbraltar - depends how long you get ashore, but to do all the things available (upper rock, caverns, monkeys etc) a trip is worth while. Walkable if you want to do your own thing. The Almeada gardens are worth a visit.

How exciting for you! We've never been and are looking forward to your review upon your return.

Florence is 1 1/2 hours from the port, take a ship tour or consider Pisa or Lucca.

Genoa. We went last year without much research and just walked the city. That was a mistake. Do some research on excursions.
Marseille. The city centre is not close to the cruise port so you need a shuttle into town or again a ship tour. We took an Uber to Aix en Provence but it wasn’t easy finding our ride so I wouldn’t recommend it unless your French is better than mine. Took a tour previously to Cassis and that was nice paired with a wine tour.

Barcelona is a great city for walking. Look for a walking tour, even the free ones are good. Ramble the Ramblas, enjoy tapas and the amazing architecture.
Gibraltar. Take a trip to the caves and WWII tunnels but watch out for the monkeys all over!