Here's another vote for Pitamakam Pass/Dawson Pass loop. I am an avid hiker and have hiked in 10 other national parks, and in the Alps and Pyranees. This hike is the most scenic and enjoyable day hike that I've been on. My experience was to perfect blue skies in early July. There was still some snow on the trail and the bear grass was in peak bloom. I encountered big horn sheep, mountain goats, and a black bear while on the hike. It just doesn't get much better than this in a day hike. I've posted a few photos at Panoramio and on Google Earth under djbouqu. If you haven't tried it, the 3D feature in Google Earth is particularly cool while viewing the GNP area.
The Swiftcurrent Pass and Gunsight Pass hikes are also amazing. I am a geologist and the geology on the Gunsight Pass hike is incredible. Glacier NP is a hiker's paradise and I plan to visit again soon.