Park naturalists lead several different hikes each day in Many Glacier Valley [1]. Hikers with a modicum of stamina and a passing interest in geology should try to catch the naturalist-led hike to Grinnell Glacier. In combination with a boat shuttle across Swiftcurrent and Josephine Lakes ($18), the all-day hike is eight miles round-trip with a 1,600-foot elevation gain. (Forgo the boat rides and it becomes 11 miles.) Grinnell Glacier reached its peak size during a sort of miniature ice age in the 1800s. Melting since then has left two smaller glaciers: The Salamander clings high on the Garden Wall; Grinnell Glacier proper is below and to the left. A warming trend starting in the 1980s has enlarged the iceberg-laden lake beneath the glacier, making it particularly hazardous to walk onto the glacial ice.
Links:
[1] http://www.moon.com/destinations/montana/glacier-national-park/many-glacier