Palermo

In 12 hours (at best) you can't even hope to cover 1/5 of what Palermo has to offer, so I would curb my enthusiasm and select just a few sights in the city to visit, at most you could also venture to Monreale to see the basilica. Monreale is only 30 min by bus on top of the hill.

Here is the official tourism portal for the city of Palermo. You can select the things to do and see from here.
https://turismo.comune.palermo.it/palermo-welcome-categorie.php?tp=68

You would not want to drive in Palermo, or spend your day looking for a parking place. I think the Ballaro market was the easiest to visit, and there are vendors and restaurants there where you can find lunch - just wander around. Monreale was interesting, but the time it would take to get there and back and actually see something would eat up to much of your day, IMO.

If you don't want to take the time to go out to Monreale (arguably the #1 sight in Sicily), you might consider the Norman Palace (Royal Palace) right in Palermo. The Palatine Chapel is really stunning.

I think Palermo is sort of known for street food. There must surely be a street-food tour or two. I think you'll find Italians take their time over meals. You may not want to sit in restaurants long enough to have two full meals during your port call. That could be 4 to 6 hours of your limited time.

I think Palermo is kind of Palermo’s best sight. Take a taxi to Quattro Canti/ Piazza Bellini and explore from there. Santa Caterina on Piazza Bellini is magnificent. From Bellini, you’re within striking distance of Ballaro and Vuccirria markets, the Cathedral, and at the head of Via Marqueda which is pedestrian only all the way to Teatro Massimo (a terrific stroll any time of day.) Wander a bit and enjoy. This center of town is very walkable. Twelve hours is plenty to see the city in this fashion. Personally, I feel like trying to see Monreale or something on your own would eat a lot of time and energy. If there are excursions to Monreale arranged through the cruise ship, that might be the better option.

If you enjoy markets, it’s not crazy to visit all three. They have their own personalities! I would recommend trying some street food at any of them, whatever strikes your fancy.

There is another post on this forum right now (posted on the Day Tours section of the forum) which includes an enthusiastic recommendation for a Palermo guide named Francesca Lombardo, with a detailed description of the time the poster spent with her. It would be good for you to read that. One idea would be to contact her, her e-mail is in the post, or a different guide you might learn about, and together choose the sites you want to visit in the time you have. With an excellent guide, you will get much more background, will not get lost, will know the schedules of any places you want to visit, and certainly find the kind of lunch spot meets your expectations, probably with great explanations of each Sicilian dish. Also, since it sounds like you need to be back to your ship by 5 pm, rush hour anywhere during the week, be careful with your timing and traffic. You wouldn’t want to be on the pier waving goodbye to your ship as it sails into the sunset.

The most important site in Palermo to visit is Monreale a short bus ride from city center. This is a “must see!”

I was in Palermo Sept 2022. I highly recommend the Puppet Museum. Thousands of marionettes through the ages. Totally lovely.

About timing. Sure, you can visit a lot of the sights and maybe even get to Monreale in those 12 hours. But an evening meal? Probably not. Restaurants in Italy don't open for dinner until 19:30 or even later, and the palermitani eat out later, around 21.00. Your best bet for an evening meal is to walk around looking for a good bar to have aperitivo (a drink and snacks).

We had 1 1/2 days in Palermo and had an awesome time. We basically followed the walk and sights listed in Ricks Sicily book and felt we had a very good overview of Palermo. Monreale is amazing, but I think you can't include it in just 12 hours - the Chapella Palentina is insanely amazing and while not as amazing as Monreale, it'll give you a good feel. I'd also recommend doing a food tour - you'll get plenty of street food as well as see some incredible sights along the way. The historical center of Palermo isn't that big so you should be ok.

My experience with cruise stops is you will have time for one or two good sights. If you opt for two sit down meals, that could be a third to half of your total time. Fine, if it's your priority.

I'm always among the first off the boat. I go to the gangway before it's open. I avoid cruise excursions. IMO they are too slow getting started and too much time is lost loading and unloading buses. Plus they will take you to a gift shop(s) for a significant part of the day.

I try to arrive knowing both where I want to go and how I plan to get there. Then hurry off the boat to give myself the most time. I also get street food, mainly to save time, because the sights are my priority.