Any international student in the nursing program?

In general there are not issues with finding a hospital that will assist you in getting a green card. If you are in a small town with only one or two hospitals, then you may have issues there, but with any big city, no issues at all. There are a couple of states right now that have fewer openings, but if you are willing to move, then there is absolutely no issue at all.

I have not run into any trouble helping students find placement when they graduate.

Some people have issues trying to find a job when they graduate, and this goes for American grads as well. It comes down to how well that you market yourself, how flexible that you are with work, etc. You need to offer something to the hospital so that they will want to hire you over some others. No different than any other field.