In reply to asdf123:
No. I just followed the traditional UKC edict of ignoring a major part of your question and suggesting something you said you didn't want!
But I figured in reality it might turn out better than some random lower rocky hill (you didn't say what altitude you were thinking of). There's just so much lower, unglaciated terrain there you could go pretty much anywhere and go up something, and it'd be over 5000m probably, but it might not be a very satisfying mountaineering trip cos it'll be dwarfed by everything around it, and the rock might be quite unpleasant and loose. And given the approaches in many valleys, you might have needed porters anyway to get to it. So...
Apologies if you've already looked, but recent AAJs have some Shimshal pics of other peaks to give an idea of surrounds. eg. http://publications.americanalpineclub.org/articles/13201215994