You will see other posts in this forum pointing to this sitehttp://www.geneanum.com/tunisie/bases.html
The site is in French, but easy enough to work through. I see that there are "Zacco" "Zago" and various other names that look close to your "Zaso".
Just a recommendation, probably the best thing if you have nnot already done it is to get the offical death record of your grandfater. The US records that I have used (also from NY) list birthplace, parents names etc. You may be able to do some research on line, but for these records I have always needed to visit the public records offices for Birth/Death/Marriage.
Regarding his immigration, you should be able to find his record at the Ellis Island website. This normally provides the place of origin (town they were living in) before coming to the us. Also the US census records from about 1900 or 1910 list year of immigration....
I hope this helps,