I would recommend you stay perhaps in Palma, and then if you hire a car you can do day trips to some really nice places like Soller or Andrax or wherever takes your fancy. Most of the resorts will be quiet, and given that Palma is a beautiful city with wonderful shops and restaurants and sights, thats where I would base myself.
You can take a train from Palma to Soller and see some of the loveliest countryside in Mallorca, travelling through the orange groves. At that time of year, the almond blossom will be out and the island looks magnificent.