Just one advice: ditch any map and just walk. Walk everywhere and anywhere, especially the narrow back streets where the locals live. The old city is beautiful and getting lost and finding your way again then getting lost again is the best way to experience it.
The medieval buildings have all been beautifully restored and many have been repurposed into boutique hotels, cafes, restaurants, and shops while new structures conform to the original architecture.
Take your time. Early morning is best so you can the city all to yourself.
Always look behind you. The view would be different.