I spent one day hiking the Bear Lake area trails: Bear Lake; Nymph Lake, Dream Lake and Emerald Lake; and Alberta and Glacier Falls. Bear Lake is a simple flat manicured trail.
One trail takes you past Nymph Lake, Dream Lake and Emerald Lake, less than 4 miles round trip. It was a wonderful trial with great views and some fun scrambling caused by snow still on parts of the trail (in late June). The trail was crowded and I imagine it is one of the most popular trails in the park.
View the photo essay for the Glaicer Gorge Trail which is also in the Bear Lake area of the park.