We've spent several weeks in Puglia but always in fall or spring. Returning for another 10 days this October. Here's my recommendations.
Locorotondo -----
Masseria Aprile
(one of the nicest places we’ve stayed at in Italy)
Matera in Basilicata ---
La Corte dei Pastori B&B
Puglia restaurants we especially liked
(all from our most recent trip in 2018 except for the last one)
Osteria Monacelle (favorite place on this trip) in Ostuni
Vicolo 45 in Ostuni (it's in a cave)
Osteria del Tempo Perso in Ostuni
Trattoria Fiori di Zucca in Lecce (outside the walls)
Pizzeria Doppio Zero in Cisternino (different ancient grains used in the dough)
L’Antica Locanda in Noci (interesting vegetables like wild grape hyacinth bulbs)
Antichi Sapori in Montegrosso (worth a drive just to eat there)
Towns in Puglia close up for most of the afternoon, maybe noon to 4:00pm, even churches. We like it that people prioritize family & eating meals at home over being convenient to tourists. We spent this time exploring the old town centers before & after lunch, & eating long lunches --- always order the house antipasti!
Alberobello — Do see both the touristy side (just try to imagine it without all the shops!) and the other side. Rione Monti is crammed with shops selling trulli knick-knacks that spill out into the streets every few feet. Walk through and try to imagine it all gone. Go to the Aia Piccola rione for a less commercialized experience & to the terraced public gardens across the main street for the best view of the Rione Monti. Eat somewhere else, like in Noci (a little west of Alberobello). If you have a car, drive all around the area to see lots of trulli in the countryside.
Bari --- Quartiere delle Orecchiette: from Piazza Federico II di Sveva you'll see the Strada Barone, & from there two little lanes that lead into the old quarter with arches. Walk along Arco Alto and Arco Basso. Explore the maze of the old town. Two churches.
Grottaglie — THE ceramics town in Puglia with lots of shops, we like Antonio Fasano shop at Via Caravaggio, 7 or 8
Lecce — maybe my favorite church facade & several cool churches, many places to eat, Roman ruins in the central piazza, great gelato, a fun town to walk around in
Matera in Basilicata — Walk all over the sassi area —- there is nowhere like it. Sasso Barisano (being renovated, shops & restaurants) & Sasso Caveoso (more like it was). Typically furnished sasso at Vico Solitario 12, in the Sasso Caveoso. Little museum full of stuff collected from the old cave-dwelling way of life.
Ostuni — LOVE the old center of Ostuni.
Otranto — mosaic floor of its cathedral (people & animals & mythical creatures)
Polignano a Mare — views, a couple hours was enough for us, tiny medieval center on the edge of the limestone cliffs, nice small pebble beach crowded in summer.
Ruvo di Puglia — 13th-century Romanesque cathedral. Museo Archeologico Nazionale Jatta has a great collection of Greek pottery in four packed rooms.
Trani — cathedral, fun passeggiata by the sea, with fishermen unloading their wares. Really interesting old town, including medieval Jewish section.
Troia — cathedral, we spent an hour or more with a marble carver across the street from the church, watching him work & visiting his workshop and buying one little piece with a carved flower on it. Unplanned, just saw the guy working there. One of those “Italy is so great” experiences.