Is there anywhere to shoot pool near bellagio?

The Italian for pool table is "biliardo" (plural: biliardi). I don't know about Bellagio, but when in town ask around for a "bar con sala biliardo" (bar with billiard room). Some bars and circoli (circles or clubs) may still have them, even in smaller towns. They were very popular at least in the 1970's and 1980's when I was living in Italy, and you could find them everywhere. Nowadays I've noticed that in many places where I used to play billiards in my youth, now they have replaced them with electronic arcades and other slot machine type games, which became legal in Italy in 2004. I guess those make more money for the bars than the old style billiards.

One thing you should be aware, is that (at least when I was growing up), the most popular games in Italy were carom games, especially the Goriziana (or 9 pin billiard). The billiard tables were the English/European style billiard tables with 6 pockets (4 corners and 2 mid table) that are significantly narrower than the ones used in the American style pool games in North America. So if you like to play the 8 ball pool, you might find it more challenging to put the balls in the pockets.

Thank you so much! We are staying at a charming place which l told my grandson had a pool table - which in fact was a pingpong table. I want to find a place with a pool table so he and his grandfather can play a game; now l know what to properly look for. We are on a hilltop above Lake Como - it is truly wonderful.