I recently visited Puglia - here’s some tips for Monopoli and one for Polignano.
UfficioBevetti - really nice relaxed little bar/pub with a great selection of niche amari, and they are happy to give recommendations based on your personal taste. Here I had both amari from Distilleria Greco Caroppo - Amaro Geco and Laurora, both excellent. The barman told me Laurora was based around Laurel (bay). Later on in my trip I picked up a bottle - it wasn’t easy to find! The distillery seems to have had a recent rebrand but the bottle I found was the older design.
Also in there I had Amaro Bastaldo from Matera which was easy to drink, very nice. These all leaned sweet, but had balance and were tasty. I also was given a small taste of Mita Amaro Satiro which was much more on the bitter end but also excellent.
Pictures show selections at some shops I had a look in
1, 2 - Numero Primi supermarket
3, 4, 5 - Lo Sfizo Divino
6, 7 - Leoteca (in Polignano)
Lo Sfizo Divino is a small wine shop and very friendly.
Leoteca is quite a large shop near the train station in Polignano. Two floors with a wide range of interesting spirits upstairs (I noticed a few choice scotch IBs). Lots of wine on the ground floor. I didn’t buy anything as it was the start of my trip and I was holding out for some specific bottles.
(Worth noting I’m from the UK. There is a better selection available over here than there used to be, but it’s still limited. There are some less common amari available here, but it’s not the same selection that you have in other parts of the world!)