Puglia for one week in late February

Grottaglie is a pottery town with a nice ceramics museum. The pottery makers are clustered in a picturesque quarter. However, you can see it in half a day; and I don't think it would make a good place to stay. You could do a day trip to it from Alberobello.
The coastal towns might be very quiet in February. We were in Puglia in late April, and much was still closed down along the coasts. However, people in the larger towns and cities like Lecce were going about their normal life. I'm not sure of the driving time between Alberobello and Lecce, but I think we decided it was longer than we wanted to do rt in a day. If you decide on staying in Lecce, pm me for the name of a super b&b that has its own parking.

ViaMichelin says you can get to Lecce is about 1-1/2 hours, so I think it's doable as a daytrip from Alberobello. However, there's a lot to see in Lecce (and you can sign up for a walking tour at the tourist office), so try to get an early start that day. Lecce has a large historic district, which is very enjoyable for just wandering.

I suggest visiting a book store or library to pick up a comprehensive guidebook to Italy that describes Puglia. There are many interesting small towns, including Otranto and Gallipoli, but the latter are down near Lecce. I don't know that you want to take two daytrips down there from Alberobello. You might be better off not spending four nights in Alberobello, which can be accurately described as "unique" but can be seen in considerably less than one day. I note that Matera's only a bit over an hour from Alberobello by car. I'd be inclined to spend the night in only one of those towns (probably Matera) and make my second base somewhere farther south, more convenient to Lecce, Gallipoli and Otranto. In fact, with a car at my disposal to ease the relocation process, I'd be tempted to stay in three different towns.

Except for Lecce and Bari (which I've heard is interesting but haven't seen), most of the tourist spots in Puglia are quite small and can be seen in 2 to 3 hours at the most, so you can take advantage of your car and see three in one day. But you'll want to select clusters that make sense from the transportation standpoint. A week is long enough to give you a really good look at Puglia if you don't have to spend too much time driving back and forth on the same roads to reach distant destinations.

Take a tour of the Sassi in Matera, and take one of the minibus tours to the area across from them, although a private guide would be better. The evening passeggiata includes everyone - tourists, locals, teens, older folks - down the Main Street to the terrace overlooking the Sassi.

Alberobello has lots of neon now, but the hill towns around it are beautiful. Martina Franca, Locorotondo are just a couple that are nearby.

Bari has a very interesting old town with cave homes; typical foods are orecchietti with broccoli rabe, all types of seafood, and a double-crusted onion pizza with black olives.

I agree that 4 nights is a lot for Alberobello. I know you already have lodging, but if it can be changed, you might consider staying in a masseria for a couple of nights ... that's the Puglian equivalent to an agriturismo. There are lots of them in the Valle d'itria. Ours was near Torre Canne. You might want to find one a bit further south, maybe around Ostuni?

We visited Puglia in October and Otranto was dead and not very charming -- I would expect to find the same in February. One of our favorite stops was Galipoli. Very picturesque. It's a fishing village, and we enjoyed watching the fishermen unload their catch, and eating very fresh fish at the restaurants there.

Lecce is full of churches, if you're interested in architecture. Many people find it a challenging place to drive. Not one of our favorite places.

Wherever you go in Puglia, be prepared for the "siesta" hours ... the restaurants & shops tend to close around 2 pm and not reopen until after 6. In Lecce, you cannot find any food after 2 pm, until restaurants reopen at 8 pm. So if you do a day trip to Lecce, be prepared with snacks in your car.

Thanks all, I have rearranged my lodging based on your feedback- we now have 2 nights in Alberobello & 2 in Matera, with 2 in between to be determined, maybe Lecce, maybe a Masseria in the southern part of Puglia. Thanks- any more suggestions are greatly appreciated! Robert

A note on Matera: the Cathedral has been reopened after many years.