My name is Tony Turini also. I'm fairly new to researching my family history. I came across your post just through searching around on here. I don't know where my family came from before they came here to America, but I would love to learn.
I know only as far back as my great grandfather who was a coal miner in a small town in Illinois that had mainly an Italian population. He died in a coal mining accident in the early 1900's when my grandfather was only three years old so he never really knew much about his history. I've been to his grave site and his last name on his tombstone is actually spelled Torino. So I thought we may have either been from the city or Torino in Italy or Turin but I'm not sure.
I got on ancestry to see if I could find a place in Italy where there was a large Turini population. It is very interesting to see that your family may have been from Austria. that would make sense being that they are so close to each other and from what I understand the borders have changed many times there over the years.
Like I said I'm fairly new to this any suggestions you may have to help me would be greatly appreciated. I hope your search is going well.