New York is a great place to live.
New York is a great place to live in.
I've seen the former usage a lot and I've started wondering what the grammar aspects of it are.
Both sentences are equally correct, right? But are both equally formal as well? What could you tell about the grammar of the former sentence?
Edit: I'm adding some more examples of similar usage:
This organisation is a great place to work.
This is a great place to stay/sit/study/travel/go.
Just to show that 'live' isn't special in this case.