Darjeeling with its interesting history and stunning landscape has many places that might interest you.
The picture in this post is that of Sandakphu, a hill 5 to 6 hours from Darjeeling. As you can see, Sandakphu is very close to the snowy mountains.
Given below is a link that would give you an idea of the variety of places to visit in Darjeeling.
http://darjeeling.gov.in/darj-tour.html