It doesn't go to a peak, but this is one of the top hikes in Glacier National Park.
The Grinnell Glacier trail leaves from the Many Glacier resort and is flat for a couple miles before finally gaining some elevation. While the initial part goes around a lake and is attractive, you can also cut off some distance if you have a boat reservation.
Then, you get to an overlook of the glacier and you can continue on and get closer to the glacier itself. I would have tried to walk on the glacier except getting to it would have required swimming or at least wading up to my head in frozen water. Due to thalassophobia and a desire not to become hypothermic, I decided against that. However, if there are at least three boats and first responders, I'd be interested in paddling to the glacier.
In any case, if you just stop at the sign at the end of the trail that's good enough. While there's no peak to bag, it's a very enjoyable experience. And, it wasn't as cold as the pictures might make you think since this was late July.
Someone on the same trip who'd been going to Glacier for years said that Grinnell had receded dramatically from what it was before and that decades ago the glacier had started at the sign at the end of the trail.
