Earmountain has it right, Grab a copy of climbing Glacier park Almost all the peaks in Gacier have non technical routes on them. Depending on what area you go to, you may need ice ax,/crampons for Glacier travel. Mid September, can be snowing, can be wonderful warm weather? in the past, I have had some of my best climbs in september,Indian summer comes early in Montana, usually mid september. The rule of thumb for Glacier was by October 15 winter has come. Soooo many mountains to climb in Glacier, where to start? If your looking for REMOTE? Drive up to Bowman lake, or Kintla lake, and take off from there.( more bears than people) From bowman you can climb Rainbow peak which is a great 4th class climb. From Kintla lake, there is Kintla peak, Kinnerly peak,and many more, the further east you hike.
Other options are the Two medicine lake area,start hiking west, notable peaks Rockwell, Rising wolf, painted teepee.Go over the pass,(don't remember the name) and drop into The Vigil, stimpson peak area.So many peaks to climb in that area! Very Remote!
Other great option, Hike 6 miles to como lake Chalet set up base camp. climb edwards, lincoln, gunsight, little matterhorn. The west ridge of edwards is one of my personal favorites! easy 5th class on good rock.