My great grandparents were immigrants to the US from Italy
Ah, I guess that makes you Italian! My grandparents are Irish.
That is correct, and you would be Irish (or at least half Irish).  
Yep! I am actually heading to Ireland for the first time in a few weeks. I have never heard the Irish language before, looking forward to that. 
That is great.  My wife and I honeymooned in Italy.  It was a fantastic experience
Italy is on the bucket list too. Have you travelled to Ireland?
I have not, but we have friends that have.  It looks like a beautiful place.  I have family in Scotland
Our conversation makes me think of the movie the Bucket List. It's pretty funny. Have you seen it?