If the option of a domestic flight is in your book, Sicily, even just for few days, will deliver great places to be and a different feeling.
Otherwise, Puglia, from the tip of Leuca up to Otranto, Lecce, Ostuni, Alberobello, Trani won't disappoint.
With the possibly one of the finest food offer in Italy.

Trani, in the northern part of Puglia, is 400 Km. from Rome, all highway.