One month in Southern Italy itinerary feedback-Puglia and Campania

I love cities but you have way too much time in Bari.Old town is nice but it is a large jumble of a city.
Take some of those days and stay in Polignano a or Monopoli, seaside, charming and on the train line.
Too much time in Matera!! One day was more than enough for us.
Not too much time in Lecce. Beautiful, classic town, lots of Baroque architecture.
You have so much time in Puglia which we loved. Maybe consider two weeks in Sicily as well.

I would love that amount of time in each of those places, but since you will not have a car and expressed slight trepidation about getting antsy, I would at least ponder if you should add a couple other stops because the public transport can be a bit onerous in Puglia.

1) Naples: you will never be bored in Naples. If you hate it, you'll still have the day trips. No change suggested. Check out the website Napoliunplugged for lots of ideas.
2) Bari and environs: Gargano is a looooong bus ride, so this is where you might insert an extra stop. Elizabeth Minchilli is a food writer with family in Bari, and her website might give you some ideas. If you nix Gargano, you might split it into Bari and one other place (I loved Monopoli).
3) Lecce is fabulous. You could add Otranto as another day trip, and perhaps look into some small tours so you can get out and about in the Salento. There is a little place called Galatina that I hate I missed, but I just don't know what the transport is like. This is a company I have noted but never used their services: https://www.espressinotravel.com/day-tours
4) I loved Matera so much I went twice, but I would delve into your day trip options here as well. There is plenty to occupy you in the town and it really is lovely, but most people see it in a day or two so just want to meet your expectations. Altamura is a day trip option that I think is fairly easy. I visited Craco and Laterza, but I had a car. I had a great tour with Antonio (this website used to be in English, so perhaps it is in the works: https://www.materatourguide.it/). They offer sassi tours and walks in the countryside to cave churches, which I recommend.
5) Salerno: try to get to Paestum--fantastic temples!

I am SO envious of this trip. I almost always advise slowing down, staying longer in places, but when you are traveling solo and relying on public transport, sometimes it does make more sense to move more and enjoy the change of scenery in the evening. I don't think you will be unhappy if you don't change anything though.

i just got back from spending 14 days of my 57-day trip in southern italy. in calabria i spent a couple of days in reggio calabria. my real target was stilo and the byzantine 'cattolica di stilo'. next, i based myself in bari for 6 days and visited barletta, trani, biseglie, molfetta andira, ruvo di puglia, bitonto, bitetto palo del colle, altamura and gravina. all were rewarding in their own way, my main interest being churches and medieval architecture. after a detour to malta, i stayed in lecce for 4 day. it was lovely, especially the old center. from there i made day trips to ostuni brindisi, otranto, galatina and gallipoli. i then went to matera for 2 days on my way to central italy. i avoided alberbello.

photography is my hobby and visually puglia is stunning. my favorites were gravina, ostuni, lecce, and matera. all the place i listed are accessible by train and can be done as day trips for bari and lecce. i consider myself a slow traveler. i wish i had explored calabria more but public transportation (my only means of travel), especially bus service seemed limited. there is a rail line all along the southeastern coast but to get to the many hill towns you would need to use the roads.

if you need more specific information let me know. enjoy and stay safe.