The castle ruins themselves are sparse, just a few fragments of Norman masonry, but the headland they sit on is exceptional. Walk up Castle Hill and the whole of Tenby's geography reveals itself: North Beach to one side, South Beach and Castle Beach to the other, and St Catherine's Island sitting just offshore.
Free to access, almost always windswept and almost always worth the climb. The museum at the base is small but gives the town's history some useful context.