Lots to sees make sure yup plan in advance to fit everything in: don't just discount it because the cruise port doesn't do the city justice, it is beautiful and interesting, but do your homework. Don't bother with proper tours, just get the shuttle and a guide book.even if you don't intend on doing much, it's worth just having little walk through town!
Get a public bus (right outside the port terminal) into Palma and go in to the cathedral (6e), then walk through the streets to get some food from a small Plaja, avoid the Major because it is overpriced! Then get a taxi (6-8e) to Castell Bellver (3e) then walk back through the grounds (easy to walk back as you take a short cut path that takes 15 mins to get to the main road, and a further 15-30mins to the ship (depending how fast you walk!). Might be better to get a bus to Porto Pi if you want to shop as it's 5 minutes walk to the ship so not far to carry your bags!