Glacier NP & the Going to the Sun road is now open as of today.
Beartooth pass is neat and a must at least once to do. Its approx. 1- 1 1/2 hrs to Red Lodge from Billings. Get gas there as its the last before the pass. Check to be sure the pass is open also. It closes all the time. Red Lodge HD is a boutique you can get your "I survived Beartooth pass" shirts.

It will take about 2 hrs to do the pass esp if you stop and take pics. 'Top of the world' store is up at the top also. Neat place for a break and a pee break (outhouse) and souvenir. On the other side of the pass it splits to Cody WY which is Chief Joseph HWY or Cooke City MY. CJH is a must and far better then BT pass. Its 3 hrs to Cody from there. Great town with a lot to do and see. There is part of the road that is under construction due to a collapse but its passable. If not Cooke City MT is 5 miles or so. Great town esp at night. Remember you are in grizzly bear country. The Miners Saloon might be grilling up ribs outside. Really good! From Cooke City you are 5 miles to Yellowstone. Its a full day 8-10 to do YS.
Inquire locally each time you do the Pass due to it maybe closed even after you go over. Snow can still happen in Cooke City as it did a few days before we got there in Aug.
Billings to--
Beartooth Pass 1-1 1/2 hrs
Cooke City MT (other side of the pass) 3 hrs
Cody WY 4-5 hrs
Yellowstone 3-3 1/2 hrs
If your into some good Italian food, Bruno's Taste of Italy is a small place on the other side of the interstate from G-0. Its in a little strip mall. Some of the best Italian we have had. The place really surprised us!