Contrary to the city, there’s not much remaining of the castle.
The only thing that’s still proudly standing is (of course?) the church: Hagia Sophia
While Mystras, the the most important Byzantine city on the Peleponnesos in its era, is deserted and in ruins today, tiny Monemvasia’s fate is completely different. Not only is the island, connected to the mainland only by a bridge, still inhabited, but it’s cobble-stone streets and tiny alleyways form a major tourist attraction.