Bari has become a very touristy area in recent years and finding a good, reasonably priced hotel can be tricky, particularly in September. We recommend that you book your hotel well in advance.
We suggest below a list of possible hotels (not far from the conference site):
Aparthotel Palazzo Calò Bari
https://palazzo-calo.barihotels.org/it/
https://palazzo-calo.barihotels.org/en/
Dilman - Luxury Stay and Lounge in Bari
https://www.dilman.it
https://www.dilman.it/en
Hotel Excelsior Bari
https://excelsiorbari.it
https://excelsiorbari.it/en/
Residence Zodiacus Bari
https://www.residencezodiacus.it
https://www.residencezodiacus.it/en/
Hotel Moderno
https://www.modernobari.com
Residence Moderno (15 minutes walk)
https://www.residencemoderno.com/
Hotel Boston
https://www.bostonbari.it
Hotel Bari Oriente
https://ih-hotels.com/it/i-nostri-aberghi/bari/ih-hotels-bari-oriente.html
https://ih-hotels.com/en/our-hotels/bari/ih-hotels-bari-oriente.html
Grande Albergo delle Nazioni (5 stars, 15-20 minutes' walk)
https://ih-hotels.com/it/i-nostri-aberghi/bari/ih-hotels-bari-grande-albergo-delle-nazioni.html
https://ih-hotels.com/en/our-hotels/bari/ih-hotels-bari-grande-albergo-delle-nazioni.html
Hotel Mercure Villa Romanazzi Carducci (4 stars, 15 minutes' walk)
https://www.villaromanazzi.com/it/
https://www.villaromanazzi.com/en/
In addition there are many B&Bs easily found on the web (not far from the conference site).
The following chain of B&Bs offers discounted prices if at the time of booking you indicate that you are attending the QuantHEP conference organized by the Department of Physics and by the INFN
prenotazioni@gattobianco.com (attn. Ms Carlucci)