Girona's old town is compact enough to explore on foot in an afternoon, though the density of interesting streets and buildings rewards a slower pace. The Onyar River divides the modern city from the medieval core; cross any of the bridges and you step into a different world.
The Cathedral staircase is the obvious starting point. From there, walk down through the Jewish Quarter and along the old city walls for the best overview of the rooftops. The Benedictine monastery of Sant Pere de Galligants, just outside the old walls, has outstanding Romanesque cloisters and a good archaeology collection.