Camp at Many Glacier, take the east side tour bus up to Siyeh Bend* bus stop. Get off the bus there, hike over Piegan Pass, past Morning Eagle falls and back to the campground. You could take the boats across the two lakes and save a few miles of hiking. The boat token is a 5/16" washer, or you can pay cash.
This has "nothing" to do with cycling, but it was one of the best hikes I have ever done in my life. And, oh, don't go to Cracker Lake.
*I think it was Siyeh Bend.