For history & culture, Minčeta Tower is hit or miss.
The literal high point of the walls walk, with the broadest sweep over the whole Old Town and out to sea, and a crenellated crown that defines Dubrovnik's silhouette. The honest catch is you reach it only as part of the full walls circuit, so its 'worth' is bound up with the €40 summer walls ticket and the climb to the top in summer heat. The view from up here is the best on the loop.