Deya (Deia) in the northwest is beautiful and really interesting, (fabulous hotel La Residencia, but lots of more reasonable places). Robert Graves spent years there, raising a family, (see his son Tomas' book 'Tuning up at Dawn' for a real onsight into the village.)
More practical might be Port Soller, and it's inland sister town Soller. There is a little train between the two places, and the famous lemon train to the capital. Loads of great restaurants and all within about half an hour's drive from Palma.