We are going to cruise around Italy. Are we allowed to bring wine back on board & take it to our rooms?

Unlikely

We just got off Norwegian Jade yesterday. You are in for a real treat. To answer your question... I don't recall which port it was, but I did see a sign indicating that you could bring wine back onboard if you paid the corkage fee. (I actually thought of you when I saw it!) You might want to verify this while on your particular sailing in case there are any changes.