We stayed in Rising Sun CG (east side, by St. Mary, no hookups). Can walk to the boat dock for a morning ride (highly recommended). Take the hike at the turnaround point.
Easy drive across Going-to-the-Sun road, but also suggest taking the Red Bus tour, as it is narrated. Lots of wildlife, so kids can be watching for mtn. goats, bighorn sheep, and bears. We saw all, plus moose and elk.
Also easy drive to Many Glacier, and more wildlife.
Take the kids out about half an hour before sunset, and watch for bears and moose around Lake Shurburne (Many Glacier Road). Tell them to not let a grizzly sneak up from behind. Really, there is lots of wildlife to see.
East side of Glacier is less-crowded than the west, but it also has fewer distractions. That's why we stayed on the east side. The best activities are driving to see as much as you can, and hiking to see even more. Logans Pass has trails heading out in multiple directions.
Enjoy!