It is not much of an animal park.  I have been there a
dozen+ times in the past 35 years and have never been
impressed by the critters.

Glacier has goats and sheep (well, so does Ohio), and
it has squirrels, chipmunks, marmots and bald eagles
(ditto, Ohio).  _Nobody_ comes to Ohio for a vacation,
least of all to see the animals.

And Glacier has bears.  However, the bears in Glacier are
best avoided.  If there are bears on a trail the park
will close the trail.

But for mountains, lakes, rivers, waterfalls, forests, flowers,
air, wind, stars, solitude ... Glacier is one of the world's best.

September is past season, the road signs are down, the hotels are
closed, the only people are groups of school children in yellow
busses.  You will have the park to yourself - maybe 10-20 folks
camping in the whole of the park - and that feels just wonderful.

However,

Glacier's trails are starting to close for the winter,
though that has never really stopped anyone on a really nice
day.  Snow may come at any time.  The leaves are at their peak
right now, but Glacier isn't much of an aspen area - try Colorado.

About critters:

There are a few 'wild animal parks' in Montana where you can
photograph all the wild animals you want.  The cages are set up
to look like the animal was photographed in the wild.  This
is where most of the Montana wild life pictures you see on calendars
are made.

For animals, the best bet is Yellowstone.  Autumn is the best
time to go - the animals are in their prime, the leaves are
turning, the air is clear, the crowds are gone and the
animals are starting to come down from the high country
to the plains by the roads.

Glacier and Yellowstone are very different places.  It is
worth it to visit both - the sum is more than the parts.

The two parks are a day's drive from each other.
There is no posted speed limit in Montana - the phrase
is 'reasonable and prudent', just don't have California
plates.  So bring the Diablo.

Glacier National Park, Montana, has quite a bit of wildlife if you know
where to look. Scott in his answer to your question picked out several good
trails on which to see wildlife, but perhaps I can be more specific.

One trail he mentions is the Skyline Trail that leaves the Logan Pass
visitor center. Park at the visitor center and cross the road on the trail.
(Going the other way will take you up the Hidden Lake trail.) Once you've
crossed the road, continue on the trail through stunning country. If you
don't like heights, this might not be the trail for you. The trail winds
along the edge of a precipice of several hundred feet; on the other side is
a rock wall several hundred feet high. The trail is safe, mostly level, and
well maintained, at least 4-6' wide, and there is a cable fastened to the
wall on your right, if one needs it. (I was once stopped in the cliff part
of the trail by three mountain sheep rams that only grudgingly gave the path
to me, but that is another story. I also saw a golden eagle here soaring
just off the cliff face at abut eye-level only thirty feet away, but that is
another another story...grin...)

After getting through the steep places you'll enter the Haystack Butte area.
There are marmots and pikas here in the rockpiles (although right now the
marmots are probably already hibernating; pikas will still be out since they
don't hibernate. Listen for their "EEEEK" calls to locate these small
critters.  I find pikas a lot of fun to photograph.  Mountain goats frequent
this area, as do mountain sheep, but goats are more common.

At certain times of the year, grizzlies are common in this area. I've never
failed to find traces of their digging on the slopes on both sides of the
trail.  Black bears will usually be found further down and I've seen more
grizzlies in Glacier than black bears.  It's been my experience that the
Park Service may or may not close trails due to the presence of a grizzly.
Several years ago, I hiked up the trail to Sperry Glacier.  Although there
were posted signs that a grizzly had been frequenting the areas traversed by
the trail, the trail was not marked closed and I met a ranger that was
watching these two bears (a sow with a small cub) in the area through which
I hiked.  (I didn't see her, but according to the ranger she was laying
under a tree a hundred yards off the trail and she rose to an upright stance
when I walked past her.)   They may be more strict now and certain bears are
known trouble-makers and their presence often closed a trail.

Heading the other way from the Logan Pass Visitor Center will take you
through alpine areas towards Hidden Lake.  There is a very good chance of
seeing mountain goats by the time you get to the top; a hike of about a half
mile. Also watch for Columbian ground squirrels around the visitor center,
depending upon the time of year you are there, since they are common there,
but are probably hibernating by now. I once watched a peregrine stoop on a
flock of smaller birds in the pass and have photographed ptarmigan along
this trail.

The Many Glacier area, as Scott mentioned, is a favorite place of grizzlies.
Watch the slopes above the trail that heads up the valley. Bighorns in the
past were fairly common visitors to the hotel's parking lot. I'm not sure if
that is still the case, but check it with a park ranger.

The Sperry Glacier area is a great place to see mountain goats.  The trail
winds it way up into the alpine area to the Sperry Glacier Chalet; a hike of
about seven miles, if I remember correctly.   Goats are often seen around
the chalet and near the glacier, a couple of miles further up the trail.

Glacier, in my estimation, has quite a bit of wildlife, but it just can't be
seen from the road as readily as it is in Yellowstone. In fact, I've been
able to find significant numbers of animals to photograph in Glacier
everytime I've been there, but some walking is usually required.

Good luck with your trip.

Gordon Dietzman