One of my first hikes in Glacier National Park was the easy "Trail of the Cedars" walk near the Avalanche Creek Campground. This trail is handicap-accessible for its entire length, features some spectacular views of the creek itself, as shown above. The photo really shows the mist that rises above the churning waters. I love the variations in the color of the water too. I have no photo that is this good. You can see other photos at the Glacier National Park Information website. I think the best time the year for visiting is early summer, before the tourists show up and fill the campground.
The park road to Avalanche Campground opens long before the Going to the Sun Road over Logan Pass, so you can visit and enjoy without the crowds.