Some really great places to visit on east and west side of the park. Overall, more animals will be spotted on the east side of the park, better scenery on the west side of the park, jmho. If you have a truck, you can take the North Fork road when you leave Camas creek and drive up the west side of the park, then re-enter at Polebridge, stop at the Merc and have a pastry, then travel to Bowman and Kintla lakes on the park side. Both very beautiful, but wouldn't recommend doing it in a car. Some great hikes around the lakes up to a lookout or two, and then stop at the Northern Lights saloon on the way out, also at Polebridge.
Hidden Lake at the top does get regularly closed due to bear activity, but is well worth the hike of not closed, drop over the far side and hike into St. Mary's falls, also very pretty. Turn north and head up to Babb and Waterton, stop at two sisters cafe for lunch, very good eats. Just enjoy Glacier and be safe, very rare to have a bear encounter, but they do happen.
Oh yeah, and if you have a concealed permit you can pack a firearm in the park. But bear spray should be fine. The goats around the visitor center are always pretty entertaining. Or you can forget the park and other tourists and simply leave hungry horse and drive across the dam and tour all the South Fork of the Flathead drainage around the Reservoir, also pretty country. Go up to Spotted bear and around the whole reservoir.