Puglia

Everywhere has the siesta, or pausa. During that time, you can eat lunch, go to the beach. Plan exploring for morning and evening, and check opening times for places you wish to see.
Are you going to have a car?
Monopoli and Lecce would be great choices.

Don’t miss Polignano a Mare.

Yes we will be renting a car! Forgot to mention that.

If staying in Monopoli, you can visit Polignano by train if you want a break from driving that day, but for the beaches you’ll need the car. Driving in and out of Lecce can be a little hairy, but nothing to worry about. Just make sure your accommodation has parking.

to the siesta

I wouldn't use that (Spanish) world in Italy, the assumption they all spend the afternoon sleeping could be seen as insulting by many locals.

Spent about a week in Puglia recently. Loved Polignano a Mare and made that our base. People are generally very friendly and it's a low key area that is very walkable.

Bari is fun and vibrant but much bigger. Not that impressed with Monopoli, Ostuni, Cisterna, Lecce etc. Enjoyed a few hours at Alberobello - definitely touristy but cute. Matera was hard to get to, and not really worth the effort. Enjoy the local food. We were also able to go to a fresh fish market in Polignano and get fresh sea bass for 4 eu then cook them in our apartment.

Note that the trains are not always on time, but generally you can shoot up and down the coast from Bari to Lecce easily - but toward night the frequency of trains decreases so make sure you are not stuck somewhere

Our experience? We loved Puglia. No car - traveled by train. So easy. Had the Trenìt! App on phone. The latest a train arrived was … 4 minutes. We spent 2 weeks touring Puglia.
Flew into Bari , train to Polignano a Mare 1 night, to Lecce 4 nights ( went on food tour , amazing churches, Roman ruins in town center, best passeggiata), to Grottaglie 3 nights ( our favorite- over 50 ceramic artisans - incredible), 3 nights Ostuni (great food, great walking town, nicest people, and so beautiful ) 2 night Monopoli (stunning sea color, great seafood, a lovely church, sea glass on beaches) , 1 night Brindisi (liked it more than we thought we would).