Viterbo is a lovely little town, pretty much overlooked by foreign tourists -- fitting at least one aspect of your specifications. It's one of the most carefully maintained medieval places of some size in central Italy, lots of old churches, narrow medieval streets with arched doorways, lions carved on just about every conceivable surface; and then there's the Palace of the Popes. It's a dormitory town for rich Romans, especially in the field of the arts, movies, etc.; as you might expect, good restaurants, and a cultured city, concerts and so on. In itself, Viterbo is well worth several days' stay, to say nothing of all the sights in the immediate area, which include most of the best Etruscan stuff anywhere.
   Easy to get to from Rome: train line (a private line, not the FS) from its own station at the Porta Flaminia, with very frequent trains, averaging every fifteen minutes thru most of the day.

Ventimiglia is another ball of fur. The town itself is overshadowed by its traditional rôle as Border With France; there's a lower town with the train station and many, many cheap to medium hotels, and — last time I was there, which was before the unified eurocurrency — most of the other buildings in the lower town were given over to luxury goods that were far cheaper in Italy than in France since the French had a history of artificially maintaining their currency high. The bustling border-town markets of Ventimiglia may now be a thing of the past.
   The upper town of Ventimiglia, on a fairly steep hill on the other side of the river, is a very moldy, decayed, and poor-looking sort of place, with a great deal of atmosphere, beautiful views of the sea, and a Roman theatre.
   All in all, I'm not sure I'd actively recommend the place, but it's not bad by any means: I personally like it, as you can probably tell. It certainly is not the run-of-the-mill tourist destination, either.