17 Nights in Puglia - What 4 or 5 Cities?

Will you have a car?
As far as your home search, do you prefer cities? Most people do not put Bari or Brindisi on their list (though I rather like Bari and think it is much nicer than most seem to).
I would make your list with your specific interests as far as home seeking first, and then break it up by region. So, somewhere near Bari for the north (plus do hop over to Matera), somewhere in the Itria Valley, somewhere in the Salento, and somewhere on the sea.
You list looks pretty good, but I would want to stay in a smaller village also, look at the Itria Valley especially for that.

We won’t have a car per se but thought we would try to rent one for the day trips when needed.

We like both large and small cities. We like to wander beautiful old towns and we love the sea! Of course we love good restaurants as well.

Public transport can be tricky in this region, so your list probably contains the best bets. Others you might consider are Gallipoli and Martina Franca. Look over the regional train/bus websites as well as the Trenitalia one so you can get a sense of the best bases with that element in mind. Even if you are stuck in place, I would choose at least one small place to rest. Not than any of these others are vast metropolises, but the contrast will be evident.

http://www.ferrovienordbarese.it/home
https://www.fseonline.it/index.aspx

Good luck. I am completely envious and hope to hear how it turns out!

My husband and I were in Puglia last October for the first time and loved it! Also went to the Amalfi Coast as we love it here. We did have a rental car the entire time we were in Puglia as yes, public transport can be tricky here. The Lonely Planet Southern Italy book is a good resource for the region. We did not go to the Gargano. Flew into Bari via Rome and picked up our car at the airport and drove to Trani which is about 35 miles N. of Bari. We used a tablet for gps and it worked beautifully. I know you said you wouldn't have a car the entire time but I will post our itinerary that we did with a car, Oct. 3-24 incl. travel days so we had 20 nights:
3 nights, TRANI, a cute seaside town with a beautiful cathedral right on the water. Daytrips to CASTEL DEL MONTE & RUVO DI PUGLIA, with it's Romanesque cathedral, and BARI. Left our car parked and took the train to Bari. Bari does not get alot of love but we really enjoyed our day here.

Enroute to the Val D'Itria we stopped at CONVERSANO and POLIGNANO AL MARE.
5 nights, VAL D'ITRIA, stayed in a trulli outside of LOCOROTONDO. From here we visited:
GROTTO DI CASTELLANA, LOCOROTONDO, MARTINA FRANCA, ALBEROBELLO, OSTUNI, CISTERNINO, MONOPOLI. The bombettes and rosemary roasted potatoes in Cisternino were so delicious!
4 nights, LECCE, From here did a daytrip and drove the Salento counter clockwise (thanks Laurel for that advice!) visiting GALLIPOLI, SANTA MARIA DI LEUCA & OTRANTO.

Stopped in the ceramics town of GROTTAGLIE enroute to Matera, where we picked up several pumi, the symbol of good luck seen on balconies in the Val d'Itria. You can also buy them at other shops in Val d'Itria towns. I know Matera is not in Puglia but is in Basilicata and absolutely worth a visit of at least 2 nights.
2 nights, MATERA, stopped at the IL Belvedere Al Parco Della Murgia on our way out of town enroute to Paestum.
1 night, PAESTUM, have always wanted to see the ruins and after a number of visits to the Amalfi Coast had not made it here yet so this time we did!
Drove the Amalfi Coast and got rid of our rental car upon arrival in Sorrento.
4 nights, SORRENTO
1 night, NAPLES, 6.30 a.m. flight
Hope this helps. Let me know if I can be of further help!

This is so helpful! Your trip sounds amazing! We are flying into Brindisi. We will re-evaluate the cities we will stay/visit. Thanks for the info.!!! I’m basically just trying to figure out which cities to stay in and how long to give each one. Love the suggestions.

Another resource I used to plan this trip besides the Lonely Planet "Southern Italy" book was the Lonely Planet "Italy's Best Trips" book. My book is from 2013 but I see there is a new version on Amazon but prob. hasn't changed much.
https://www.amazon.com/Lonely-Planet-Italys-Trips-Travel/dp/1786573210/ref=sr_1_1?ie=UTF8&qid=1525197249&sr=8-1&keywords=lonely+planet+italy+best+trips

You will love Puglia!

In three trips to Puglia, we have visited all the towns you mention, plus quite a few more. We have stayed in Trani, Ostuni, and Lecce for a week each and I can well imagine being able to live in all three. Bari, too, probably. If I had to pick just one for beauty, convenience, transportation, food, and lots of things to do, I'd pick Lecce.

Also check out Giovinazzo up the coast from Bari --- never been there, but we'd like to next time!

Will you be staying in the historical centers of these towns?

Just checked the table of contents on Amazon of the newer edition of the L.P. Italy's Best Trips and it now includes a section on "The Val'd'Itria." Almost double the pages devoted to Puglia that the 2013 book has.

Giovinazzo is quite pretty also. We stayed there a night since it is so close to the airport.

We just got back from a great 22 day trip flying to Naples and returning from Bari. We spent 4 nights in each of Lecce and Locorotondo. Both were good bases. Lecce we did a one day bike tour to the coast and another day on a minivan tour organised by the TI which took 9 hours do a loop from Gallipoli along the south coast to Otranto and back.

Otranto was underwhelming - Gallipoli nicer. We spent a few very nice hours in Ostuni on our way from Lecce to Locorotondo. Did that by taking train, leaving bags at Ostuni TI and then prearranged taxi to Locorotondo.

In Locorotondo we did day trips on foot and by rental bike. For example bike to Martina Franca, then to Alberobello (o my the tourists! Give it a pass and see the Trulli with walks in the country) and train back to Locorotondo. We spent several wonderful hours doing countryside walks down back lanes with the longest outing to Cisternino (underwhelming) and train back.

While not part of Puglia we very much enjoyed 3 nights in Matera - an easy train ride from Bari.

Enjoy!

You can easily daytrip from Lecce to Otranto and Gallipoli, both of which, in my opinion, are too isolated to consider as home bases. We visited both on day trips and were not particularly taken with either, though I think the fact that the wind was blowing approximately 100 mph in Gallipoli contributed to that. I'd consider staying in Trani (which we loved) and daytripping to Bari. We're not in the majority on this, but we enjoyed our daytrip to Brindisi and thought that might have been a good place to stay. We have not been to Monopoli or Polignano a Mare, but we know people who have really enjoyed those spots. I agree with the poster who loved Locorotondo; we thought we would have enjoyed staying there. You'll have a great trip no matter where you stay. It's a wonderful part of the country to visit.

Add Matera to your day trips; well worth spending a night so you can use one of the cave hotels (of which there are many). Unique area with a history.