We really enjoyed walking up to the top of Dalt Vila. The climb is steep in places, but the are plenty of places to stop off and rest before continuing. The views from the top are fantastic, well worth the effort.
I'd recommend wearing sensible shoes, I had no problems wearing trainers but saw people in sandals slip on the smooth parts of the path.
There are plenty of little streets and alleys to explore. One street in particular has a lot of bars, restaurants and shops which all look really lovely. We stopped off for some well earned tapas and cocktails on the way out.