As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
If you run Ragusa in this surname distribution map (put it in where it says cognome), there appears to be a heavy distribution in Sicily. So, yes it would imply that your lineage comes from Sicily. The problem is that some surnames are very common and have wide distribution. There looks like a heavy distribution in the North as well. Now this could be from people moving or it could be that there are several branches from that surname.
Maybe one of our Italian members can respond with an little more detail and knowledge than I can.
This might not be your case because the history of surnames in Italy is a complicated subject. In many cases people who had surnames with the names of geographical places (towns, localities, regions) like Ragusa, Messina, Napoli, etc.were of jewish lineage. In 1492 the spanish kingdom initiated the expulsion and persecution of jews from Spain and related places under spanish rule, such as Sicily and Sardinia. As jews started to migrate north and east, many took the names of the towns they were from. As I said, this might not be your case but there could be a definite possibility to a remote jewish lineage.