Not far. Maybe 1 mile as the most.  However, there is a valley floor that separates the two.

Pull up Google maps. Zoom in to State College.  Then look for the two towns that I mention. 

You should be able to find them.  If you are looking on the format where you can see topography, you should be able to see the ski slopes.... I guess that might depend if you know what to look for.

edit: Google maps show The Lodge at Tussey Mountain. That is where the ski slopes are located at.

It also has a place labeled Mt Nittany Conservancy.  That is on Mt. Nittany.