How can i find out where in italy im from?

my great grandfather came from italy, i know it was in Piedmont somewhere, my gram isnt sure what village, my great grandfather first came over threw Argentina so it wasnt threw ellis island, but then he returned to italy, and came back to america this time threw ellis island, my grand mother told me our name got spelled wrong im not sure if this is true or not, none the less, i know which way either name is to be spelled, but is there a website to see where exactly i came from, also if i find out where i came from, is there a way that i could apply to be an italian citizen or it doesnt work unless im full italian