Etes-vous flamand ou walon?
Il importe peu, trois Américains parlent français et personne ne parle flamand.
Je suis né près de Metz.
I was looking at your schedule and think it is more likely that you will be in Glacier in August, not Sept.
Also, like everyone else - you simply cannot miss Glacier and Going to the Sun.
That said, I would strongly urge you to consider a few days at Many Glacier.
Many Glacier is just north of Going to the Sun and the center for great hiking.
There is hiker/biker camping, camp store, showers, boat rentals, a pizza café, and a fine hotel.
And the hiking is out of this world.
Unless you absolutely must visit Missoula, I would suggest riding from Yellowstone to Glacier on US 89.
Between Gardiner and Livingston there is an old road on the east side of the Yellowstone River thru Pray.
Then US 89 via White Sulphur Springs has very little traffic and huge views.
It gets a little busy heading into Great Falls (The waterfalls on the Missouri are "great" but less in August.)
Great Falls has nice bike shops and outdoor services.
Heading north, US 89 has wide-open views of the Front Range and light traffic.
On the west side of Browning, there is an excellent small museum of Northern Plains Indian culture.
If you have plenty of time - I would suggest riding west on US 2, then to Two Medicine.
From Two Medicine you can ride all the way up to Many Glacier on the east side.
Otherwise, I would ride IR 464 from Browning to Babb - then into Many Glacier.
I have ridden Going to the Sun Road many times - it is ALWAYS worth it.
On the east side, I like to camp at Rising Sun rather than at St Mary -
Rising Sun also has a little café and showers - with hiker/biker camping.
St Mary campground has 400 places and is a parking lot full of RVs.
Choosing the best time to start riding Going to the Sun is tricky.
East to west is the best direction because you have the morning sun illuminating the mountains.
But you want to have sun - thus, you shouldn't leave too early.
I usually leave about a half-hour after sunrise.
No big breakfast - but I do snack often on the climb.
When you get to the top there are two possible hikes.
8 million people follow the boardwalk south to Hidden Lake - nice, but.
Highline Trail heads north from the parking lot - wow!
There is a small stretch where you have to hold on to a metal rope.
But you are literally on top of the mountains.
I usually spend a few hours up top, then zoom down.
There are two good camping options on the west side.
(Apgar, like St Mary, is way too big for me.)
Sprague Creek is on Lake McDonald right next to the lodge and services.
Avalanche is a little further away but - -
The trail to Avalanche Lake is a lovely short hike in the evening.
From Glacier I would suggest taking the Northern Tier route westwards.
There is a busy stretch of US 93 NW of Whitefish with no shoulders.
There is a totally empty paved road option from Trego to Libby Dam.
I once changed pants in the middle of this road with no concern for traffic.
Unfortunately, there is no photo to record this important event.
Anyhoo, here's a couple of photos - Along US 89 and in Glacier NP -