Traveling from Cody over to Old Faithful Inn, should we take the Chief Joseph & Beartooth highway route into Yellowstone at the North entrance so that we get a chance to travel that route? I was planning on entering at the East entrance, but it seems I've heard alot about the scenic drive and am wondering if we should adjust our route? Does that double our drive time though? We will have 1 night at OFI, then 3 nights at Lake Hotel cabins before going down to Jackson Hole. So I'm not sure if we try to do this on the way in, or if we just catch some of the Beartooth Highway on one of our days touring?