You won't be able to get very close to the Winds thru-traveling; but probably your best chance for views is along US-287 between Dubois and Lander. If you want to actually drive up close to the range and maybe do some hiking, then you need to take US-191 since most access points are from the Pinedale area. I've traveled 191 in the past and don't recall being able to see much from the highway -- but I would think the route along 287 will give you some views.
You've probably already been there, but you should take the Beartooth Highway between Red Lodge and Cooke City if it's still open in late September. To get to 287 you would need to go through Yellowstone and Grand Teton and turn at Moran Junction. Be sure to look in your rearview mirror, you get an amazing distance view of the Tetons from 287 on a clear day!
To get to Red Lodge I would go to Great Falls and take US-89 all the way to I-90 east, get off at the Columbus exit and take 78 to Red Lodge.
Before you get to Colorado, the drive through Wyoming will be boring -- there's no way around it unless you wind way out of the way.
In Colorado, I would suggest traveling eastbound through RMNP and taking 7 to 72 to near Boulder. 14 from Walden to Ft. Collins is pretty nice too if you want to avoid the park.
Basically, I would suggest this route http://tinyurl.com/6jpk92