I'd spend most of my time in Glacier if I could. It's funny, but I just got back from doing one of Dave's recommended overnight trips yesterday, though I did it in reverse.
I had hoped to hike into Red Eagle early and then make it up to Triple Divide Pass before heading out via Virginia falls in the morning, but the inconsistent shuttle system and my own miscalculation/laziness to get up made that impossible before I even started. So I took it easy, taking lots of pictures and enjoying the wildflowers. There are some fantastic meadows between the 1913 Ranger Station and Red Eagle Creek. In fact, the whole section reminded me very much of hiking into the Belly River from Chief Mountain customs, minus the bugs: meadows interspersed between stands of trees, a large mountain dominating the confluence of two drainages (Red Eagle instead of Cosley Ridge), and fantastic wildflowers. It definitely gets less traffic than the Belly--which is ironic given that Red Eagle Lake is so much more accessible. But when you have campgrounds every few miles like you do in the Belly, and all of them low elevation, that's how it goes sometimes.