I understand those who say that a clockwise route is best, but it is hard to say when is the best time to go to Yellowstone -- in the summer, it is warm and crowded and there may be bugs. We were there in October, and it was very cool and not so crowded and no bugs. Plus, the cool air meant that every hot spring was steaming -- this is Mammoth Hot Spring:

If you'd like more info on YNP in October, here is our blog post, with lots of pictures:
YNP Blog PostBut it is true that as late October approaches, you are more likely to get some snow.