I am sure that there are some Italian banks with a presence in the US who would be delighted to help you open an account "remotely". For sure the Monte dei Paschi di Siena will have a presence - but they are about the most expensive bank in the world!!
Citibank operate in Italy, and banking is becoming rather globalised now - so I suggest a bit of web-based research (first perhaps having established to which of the "international" circuits your potential local branch adheres) would be your best route.
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