The neighbourhood inside the castle's walls still lives and breathes; if you walk around this busy, ancient neighbourhood for long enough you'll invariably stumble into someone's courtyard thinking it's a church or ruin (no one seems to mind, though). In spring and summer the fragrance of camomile is in the air (and underfoot), and wildflowers burst from every gap between the stones.
The highest point is occupied by the Inner Fortress, where ruined stairs lead to a Tolkienesque water reservoir. Views are spectacular in all directions, and guided tours are available from the entry gate for €10. It's a steep ten minute walk up the hill from the centre of town.