Based on your desire of including the Bear Tooth, the choice is narrowed down to Canyon. Even from here, it will be a long day to make just the top of Beartooth. I wouldn't worry about to much planning and play it by ear based on weather and traffic conditions. A herd of bison can make a two mile jaunt to the next attraction a 30 minute ordeal. Otherwise you may get upset at not reaching a destination or spending too much time driving by wonderful things.
Make sure you realize just how big Yellowstone is. On our first trip, we stayed at Madison and it took a long day to drive the north loop with only a few short hikes. It is really too big just to enjoy seeing from one location. Each time we go, we pick a different campground to explore that area. Even with each trip being 5 days, we don't get tired.
Make sure you reserve a couple hours one day just for sitting and watching wildlife.
My favorite campground though is Bridge Bay. Easy to get around to the geyser basin, large field for wildlife watching about 15 minutes north, short stroll to the lake, etc.
Top off your tank in Cody or as you leave the interstate. But don't sweat getting fuel in the park. It is a little more expensive, but reasonable considering the location.
There are so many wonderful spots to pop. One of the splendid colored pools, overlooking the Yellowstone waterfalls in the canyon, top of Beartooth or during a break on a hike. Don't recommend at Old Faithful as it isn't special with so many people around. Just hope she says "yes" or it could be a long ride home.
