Palma de Mallorca was one of our ports of call last month. If you want to stay in town, it is very easy to do on your own. As geordie mentioned above, the cruise lines typically provide a bus (at a cost) to take you to the town center. (On NCL, it was $10 per person for an all-day pass, available on the ship.) Our bus dropped us off at a promenade across the street from the Almudaina Palace and Cathedral La Seu. From there, it was an easy walk throughout the town, including a stroll down the Passeig del Born, which has a nice collection of restaurants.
Of course, as you are going in the summer, you might want to visit a beach. I wouldn't do this instead of a trip through town, but in addition to it. You can ask the shore excursion staff on your cruise for some ideas as to the best ones to incorporate into your day.