This restaurant near the sea on the edges of the old town served us one of the nicest meals we had in Italy at affordable prices. Has a seafood and regional menu.
Incidentally, guidebooks say don't bother going to Bari but to walk around and have great food and a nice old town to wander around, it is pretty good, and you can always get a cheap flight there then a train to Lecce for a day too.
Piazza del Ferrarese, 22