[markem]

Having done my share of mountaineering and also deep country backpacking, I'd say that perhaps Glacier National Park or even up to the Banff area would be incredible in October. Some good route planning and some last minute local beta on conditions should give you some really great experiences with none of the mosquitoes and few of the tourons. If you like remote as well, then maybe the Bogaboos in SE British Columbia. I've done multi-day rock climbing routes there up to early October with only mild snow to deal with.