You may need an Italian bank account for bureaucratic reasons, such as if you are paying Italian taxes or have a client who wants to pay to an Italian bank. If you’re a student or here short term, you likely don’t need one and Wise would do it. Banks will generally require a resident permit and residency. Here are some suggested by the international community.
N26 — online bank
Banca Etica — Ethical, sustainable financing
Via dell’Agnolo 73 R, Santa Croce area
Intesa San Paolo — Piazza della Repubblica 11 R
BancoPosta — Attached to the post office, so has a lot of ATMs. You can get a regular checking account or apply for a debit card that accepts money transfer payments with an IBAN.