Overall I would really recommend Nunzia and Francesco's place! The room has a really nice authentic look and is being taken care of properly in terms of cleaning, food refillments, and bed linen/towels.
Moreover, Molfetta is a small town with a nice and lovely atmosphere, even better than Bari.
Regarding the beaches in the area, I'd recommend to bring some water shoes since most of them are stone beaches.
Finally if you need tips on what to do, you can always ask Francesco as he is a local and knows the area really well which can lead you to places you wouldn't find on your own.