Orvieto is another good one, especially for people interested in religious architecture. Its cathedral is one of the best in Italy and it has a great restaurant culture and some fascinating underground tunnels to explore, but since it only has about twenty thousand people and has a disproportionately low number of famous former inhabitants, Americans in Italy often pass it by.
The façade, oh dear...
Even if the façade is too much for one (I have maximalist tastes in art so it's not too much for me at all), the spare, contemplative interior more than makes up for it.
I know a woman who swears by Durban (she talks about it as incessantly as I talk about Hakodate or Perugia), and I've wanted to visit some of the sights in western Turkey--Ephesus, Hierapolis, Konya--since seeing a travel documentary about them last year.