I recently had a week visit to Majorca (or Mallorca) before all the crowds get to this wonderful piece of the Mediterranean. The island is gorgeous and you can truly enjoy it and take a good rest if you go to the smaller villages. It's a great experience, it's plenty warm there with around 25-28C and going to the beaches you have all the space in the world. The other people there are other people who want peace and quiet, which is perfectly relaxing.
If you're going to visit the island there's 2 things which in my opinion you really should see, for that you really should rent a car though.
Caves of Drach (Dragon Caves)
These caves were unlikely other caves I'd seen, which were really boring and bland in comparison. The caves give a really "un-earthly" feeling and are wondrous to see. Plus it's a good activity while you're hiding from the sun. The only downside is that it's busy in there and you'll be walking slowly with other people.
Mountains, driving to Soller
From Palma or another town like Inca, driving to the port town of Soller is fantastic. There's a lot of viewing points and mountain lakes up there. One of them also had some local animal friends such as goats, sheep, donkeys and horses. It was wonderful to be walking around those lakes and see all the animals around.