Puglia

How much time will you have? What kinds of things do you enjoy?
Though not in Puglia, Matera would be the one place I would urge you to look into visiting en route.
You have these basic sections to choose from, somewhat overlapping of course: Bari and its environs; the Gargano peninsula, which is somewhat isolated; the Itria valley, which includes Alberobello; and the Salento, the southern tip.
For boutique hotels, see Monopoli, Lecce, Alberobello.

Pick up a guide book that covers that area. There are many attractive small towns. I like Lecce, which is a Baroque city with quite a different appearance from the cute little coastal towns.

And yes, Matera.

We did a five night trip there a few years ago. It was not enough time! I suggest two bases, Lecce for at least two nights and Polignano al Mare for at least two more. (If you have 3 nights each place, all the better.) That way you can tour the heel of the boot from Lecce, hit a few scenic towns on your way north, then stay by the seaside. We enjoyed Martina Franca, Ostuni, and Locorotondo on our way to Polignano. Castel del Monte is a nice day trip from Polignano.

We will be driving from Rome. Thank you for all the info. so far. Lecce and Matera are on our list. Anyone been to Vieste?
Taken a boat trip along coast to see grottos,etc?
We have one week following 9 days in Tuscany. We are considering flying from Bari to Zurich, where we catch our flight back to the U.S.A. rather than driving back to Rome.

A week will give you time for a nice visit, but I'm not sure about ranging all the way from Lecce to the Gargano Peninsula, plus Matera. You might be able to pull it off. A lot of the cute little towns are, indeed, little, and you may be able to walk every street in the historic district in about 2 hours. That doesn't apply to Bari, Lecce, or Matera but is probably true of Gallipoli, Monopoli, Alberobello, Martina Franca, Locorotondo, etc.

Yes, we've been to Vieste and Peschici and we enjoyed them both very much. But as someone suggested, with only a week, you may have to choose between places that are pretty far apart, i.e., if you want to do Matera you may not have time for the Gargano peninsula.

Matera is easy to reach from Bari, about an hour's drive.