Puglia Itinerary

Looks good to me.

We stayed here in Matera and enjoyed it.
http://www.ladolcevitamatera.it/

I was in Puglia in Late Sept early Oct. your itin sounds good. It will be relaxing. Do u have any interest in mosaics? They are easily enjoyed in a day trip to Ravenna. They are of a religious subject and outstanding!

It's about 350 miles from Bari to Ravenna. That would be some day trip.

I like your itinerary. Another town I liked is Otranto.

Thanks all. 2 quick questions: Is it ok to drink the water in Puglia? Will things be open late April - early May?

Be very careful about parking your car with luggage inside. I hate to be the bearer of bad tidings, and I have taken the risk several times with no problem, but car break-is in a very real risk (even in a trunk with nothing in sight).
Taranto--archaeological museum? If not, I'd not risk leaving the luggage unattended and stop in little Grottaglie and buy pottery instead (or whatever floats your boat--you will still need to store luggage if you go to the museum, and I am not sure if they offer it).
When you drive from Matera to the coast, there are some temples at Metaponto, which I found interesting. Craco near Matera is a super cool tour of an abandoned village.
North of Gallipoli there is a great park if you like nature stuff.
I find rounding up Google maps estimates works fine. The driving is easy, just a lot of traffic circles, and driving in and out of Lecce can be a little stressful but not a huge deal.
I don't like moving that much, but I get wanting a different flavor at night. It's really just a personal preference. If you wanted less moving, you probably could combine Lecce and Gallipoli, but it depends on what you had in your plans for each day.
Also be aware a lot closes from 12-5, sometimes even sites can have closings, so verify opening times of anything you wish to see.

I've not heard of a problem with the water in Puglia--or anywhere in Italy, for that matter. I've been to Puglia twice. I carried around my own water bottle, filled with tap water. I ordered bottled water in restaurants since that seemed to be the thing to do, given that I wasn't ordering wine or any other beverage one pays for.

Water, fine. AirBnB, fine.
Things will be open in late April but anywhere other than the places you are visiting will be very very quiet. All the places on your list should be pleasant--not too crowded, not too/too quiet.

We've spent about 8 weeks total in Puglia in November or late March/early April. Everything I can think of is open except for the beaches, some boat rides, and the just-for-summer parts of beach towns. People do still sunbathe or go for walks on the beach on warmer days, so many beaches are not literally closed, just not in summer mode. Even churches are often closed all afternoon, so that's when you either explore a town (despite the shops and bakeries being closed), eat a long lunch, or drive from place to place. We've never had any trouble finding restaurants open, but be aware that they are not usually open before noon or after 3:00pm --- "lunchtime" doesn't just run into "dinnertime" the way it does in the many restaurants in the States.

Google Maps does a good job of predicting the time it takes to drive from one place in Puglia to another. But, just like at home, Google doesn't "know" things like how often you will need to stop, how long it will take you to park outside the ZTL, or whether you will get a little lost (perhaps because what looks like a road on the map looks like someone's very narrow and almost vertical driveway in real life). In Puglia, it won't really be the topography or the traffic that takes extra time.

You don't say what you are interested in doing in any of the towns you name, except lunch, so I can't advise on the towns you picked or how long each will take. But, generally speaking, a definite thumbs up for spending lots of time in Matera, Lecce, Ostuni, and Bari, whereas Alberobello and Polignano a Mare seemed more like two hour visits to us. The other four towns are towns we have been to, but I'd have to look them up to be able to comment on them --- perhaps that means they weren't quite as memorable? But really, every town we have been to in Puglia has been enjoyable and you can't go wrong.

Since you do mention lunch a few times, I'll add that we've stayed in Ostuni and Lecce for a week each and can say that in both we found the greatest number of fantastic places to eat for the shortest walking distance. If you stay right in old town Ostuni, you barely need to walk for 5 minutes.

I was in Puglia in April of this year. Everything was open. Matera and Alberobello were crowded.

The water is safe to drink. Wine and spritzes taste better.

Cris, just FYI, I am also traveling to Puglia in early May, and have been so surprised at how many Airbnb's are already booked. I had no idea that I would have such a problem finding Airbnb's that looked appealing to me this early on. I have looked on VRBO also, and just googled B&B's, spending hours of time. We are a party of 3 which does eliminate a lot of places. Don't wait!