First of all, Polignano is amazing, GO AND VISIT.
Second of all, stay at Francesco's apartment!!
Francesco is an amazing host, he was really friendly and full of great ideas and suggestions on where to go on our trip. He even gave us directions to a restaurant that ended up being our favorite from our two week trip to Italy.
The apartment is absolutely fab, really clean and modern and has everything you could need. The location is brill, being 5 mins from all the activity and there is free parking around the corner.
The upstairs terrace is great if you are having lunch in, or even to chill with a glass of wine at night when you come in. There is also a really friendly old lady next door who loves a chat! :)
Definitely stay here!!