Bari or Polignano do mare

Im flying to Bari for 4 days with my 2 year old daughter and my mom. We just want to enjoy exploring civita vecchia and try some delicious food. We'd prefer to stay away from the touristy places :) I can speak Italian so I don't mind going off the beaten track

Would it make sense to get a hotel in Bitonto or Giovanazzi as a base? ( the hotels in Bari centre seem so much more expensive)

Where could we go for a day trip to see a picturesque town? Is there anything in particular you can recommend, maybe a seaside town?