I would recommend are Teix and the Archdukes pathway from Valdermossa, Cuber reservoir over Es Cornadors and down Pillgrim steps to Biniaraix then Soller.
The best Scrambles I have done on the island are the Cavel Bernat ridge and the Torrent de Parreis gorge, another good day out is canyoning in the mega impressive Torrent Des Gorg Blau Canyon/Sa Fosca but you would be advised to do this with a tour operator.
The biggest problem is getting to these routes with no car, have heard reports recently that there are too many walkers for the buses to cope with.