I'm spending a week in Bari in February and would like to make some day trips by bus or train. I'm thinking about Matera and Alberobella, other suggestions? Good seafood a plus...
Monopoli, Polignano, Trani, Locorotondo, maybe Ostuni.
Actually Lecce should be a destination to consider as well. It looks far but Bari and Lecce are connected by fast trains therefore you can get there in less than 90 min.
From Bari it's a very short train ride to Trani, Monopoli, Polignano, Giovinazzo, Barletta
https://slowtravelitalyspain.blogspot.com/2019/11/puglia-bari-in-april-trip-report.html?m=1
I'd advise skipping Alberobello. It's become a trulli Disneyland. Picturesque but slammed with bus tours.
You will see trulli along the roads in that area; it's the concentration of them in Alberobello that draws visitors, but most of them are now B&Bs, rentals, and shops for tourists. If you do go, I found the new part of town more pleasant.
I'd strongly advise overnighting in Matera; maybe travel there by bus from the airport after your arrival in Bari, spend three nights, return to Bari and take your other day trips.
Bari has some great seafood restaurants; we liked AI GHIOTTONI. But almost very restaurants in that part of Puglia will offer seafood, with mussels being very popular. Note that dishes starred with an asterisk have been previously frozen, but with the shrimp, at least, quality is still good as far as I can tell from limited experience.