Most European bank branches in Uruguay (I'm speaking specifically of Colonia) cater to Argentine and other foreign residents. Several years ago we opened a US dollar account at one of the European branches using a North American address -- no Uruguayan address or utility bill was required.
Last week we visited the branch, and the bank wanted us to fill out a new form. Again, there was no need for a local address in Uruguay. This time we gave them our address in Buenos Aires.
The bank will issue debit cards for us, which can be used internationally to withdraw dollars from our US dollar savings account. However, the bank will not send the cards to us. We must return to the branch to pick them up.
With an Italian passport, you should have no problem to open an account. The exception is for US citizens, who have become the lepers of the global banking system thanks to the FATCA (Foreign Account Tax Compliance Act) of 2010, which requires every bank in the world to execute an agreement with the U.S. IRS tax agency, or face 30% withholding on remittances from their U.S. correspondent bank.
European banks in Uruguay are most solicitous ... until one reveals the scarlet letter of the blue yanqui passport. Then the bank officer's smile instantly fades, and the would-be depositor is politely escorted to the door. There may be exceptions if one asks around ... but as always, things are changing, and not in a favourable direction.