Joel,
With two days I would do the lower loop one day and the upper the second.
There is much to see without to much walking.

For limited walking I would take 14 in to the park, when you hit the loop just after the Fishing Bridge, turn North to Canyon Village. You will go past Mud Volcano area but I wouldn't stop there, it would require a bit of walking. In the Hayden Valley you will see quit a bit of wildlife on Yellowstone turnouts on road for viewing. In July I saw a herd of 120 elk one day and another five huge bulls on another, all seen from the road. As you get close to Canyon Village turn and drive in to Artist Point. Artist Point will require a few hundred foot walk and it is an iconic view. Once you leave Artist Point take the North Rim Road, many places to stop and see the canyon right next to the road. From Canyon head to Norris, right before Norris take the one way Virginia Cascade road it is worth the view. When you get back to the main road head toward Norris, pass on Norris to much walking. Head South toward Old Faithful and stop at Gibbon Falls it is right on the main road. Pass on both of Paint Pots you see going South, to much walking.

After Madison Junction Do take Firehole Canyon Drive, head South again and do take Firehole Lake Drive. On Firehole Lake Drive, the Fountain Geyser is just off the road and if you are lucky you might get to see it. Next is Grand Prismatic and it is Iconic, but you will walk several hundred yards on the boardwalks to get to it, it might be to much walking. At Old Faithful as you are on the access road take the first road you come to. Do not go to the main parking lot. You want the access that takes you to the Old Faithful Inn and it is a must see. It is the Largest Log Hotel in the world. Old Faithful is a hundred yards away and you can see it from parking lot, plus the rest of the basin is somewhat in view. I would finish the loop if you are heading back to Cody. You just spent a long day.

If you follow the same root to the Upper Loop the next day you get to go through Hayden Valley again, then head north to the Roosevelt Tower. At the tower head East in to the Lamar Valley. No walking here as the Valley is huge and you will see most from the road. Spotting Scope or Binoculars are a must. Turn back east and head to Mammoth, drive the loop around the top of Mammoth then head in to Gardnier, Big Horns can sometimes bee seen in the valley going to Gardnier. They have a few good restaurants to. Returning that afternoon I would do the same course back if I wanted to see wildlife, but completing the loop to see it all is good as well. Also there is a road between Mammoth and Roosevelt Tower called Blacktail Plateau Drive, it is somewhat primitive and if your car is up to it you might get a few wildlife views. Day two is full at this point.

For the third day you can return to some of the favorite points.