Assuming we were going to do Cody, Roosevelt Lodge/Cabins, Old Faithful Inn, Jackson/Grand Tetons...what is the logical order to do them in based on distance?

The order you listed looks good to me.

Lee Ann

Come from Cody via the NE entrance and the Beartooth Highway.
The roads inside the park are a figure 8. You are only seeing the west side of the figure 8 but if that is what you have time for, it is probably the best route.
Are you taking the rental car back to where you rented it from or are you paying a drop fee?

We'll have 7 days not including air travel time. I was thinking:

1 day - Cody
2 days - Roosevelt
2 days - Old Faithful
2 days - Grand Tetons

Would you recommend a different part of the figure 8? If so, where?

We're ok with paying a drop fee.

I would check out Mammoth area and also the Upper and Lower Falls. There is a great short hike, via Uncle Tom's trail, to a wonderful view of the Lower Falls. I visited Yellowstone 2 years ago and wrote a trip report on the best waterfalls I saw in the park (with pictures and access information: http://livelifeoutofoffice.com/2014/...f-yellowstone/

rachill_az--thanks for sharing that link--great photos and info for our upcoming YNP trip this summer.