Don't know what are the conditions now but my cousin went to Amarnath some 2 months back. He said it was a heavenly experience. Climbing Amarnath by foot is no joke either. And according to him the security was massive there. Atleast 5000 troops were deployed their.
Anyways , how about Kailash mansarover ?? Though not comparable to Mt. Everest , it is a heavenly experience as well