Can't help with Menorca, but we found little to get excited about in Palermo. From the docks we crossed the road & walked straight ahead to the main part of town & the turned left along a busy street & walked for about 10 or 15 minutes to the Old Local Market Area. Sat down for a drink then walked back to ship taking a different route, & that was as exciting as it got for us. Good Luck.
The sail in to Mahon is wonderful- its a long harbour lined with picruresque and luxurious houses which you can almost stretch out and touch! Ship docks right in the town. We got on a catmaran and had a sail around the little bays, stopped for a swim and a BBQ- didnt go into town.
Palermo- we got one of those horse and carts for a brief trot around the old town- its like travelling back in time there- definitely godfather like!
We found palermo a let down and we tried to sek out the local culture. It was interesting to see but was hectic, crazy drivers and you take your life into your own hands when crossing the road from the port to the town. Basically its what you make it. I'm sure if you do your homework you would get the most from it. We didnt have the time before our cruise to do some homework on it but as the previous writer (Dolan) has stated perhaps a trip on one of the horse dranw carts would show you the best bits. If we went again we would do a ship excursion.
Mahon was lovely and as stated it is fascinating as the ship gracefully sails into the town centre and then does a complete turn in preperation for sailing out again. We did a ship bike tour down to the south of the island whic wasnt strenuous and was totally enjoyable and woth every penny. It took us through winding country lanes with whitewashed houses down to binebeca beach for some lunch and a swim and took a different route back. If you like biking you will love it. Enjoy!