Soller is an excellent location from which to hike. It is not necessary to hire a car as the bus service is very reliable. 

An excellent walking guide is Valerie Crespí Green's 'Landscapes of Mallorca'. It contains a wide variety of excellent walks for all levels. The walk up Puig Massanella from Lluc (the farm charges 6 euros/person each which is a bit steep - like the walk!). There is an amazing natural spring in a cave on the way up and the views are stunning. Note that the bus to Lluc stops at the end of October. 

 The walk from Soller through Biniaraix up the Camino de Barranc up to the Mirador d'en Quesada and then across the col to the Puig l'Ofre provides breathtaking views across the whole of the Tramuntana range looking down over Cuber Lake. The first climb goes up a very ancient path of stone steps passing many beautiful pools with views over Soller. The Coll de l'Ofre is stunning and very verdant in the spring and autumn then l'Ofre itself is steep but worth it. The views from the top of l'Ofre are better than from the Mirador so to shorten the walk leave out the Mirador. 

 The walk from Valldemossa up the Puig Teix and then along the ridge taking in the Carigoli and the Mirador de ses Puntes is also beautiful. Unfortunately the Teix peak is closed unless you get permission from the landowner (from a restaurant in Port Soller) but the walk is spectacular with great views without this although not to be done on a very windy or misty day since at one point the path has a sheer drop on one side. Compared with the other two walks this one was less demanding in that it was less steep and the climbing more spread out but equally beautiful with impressive views of the coastline.