The Grand Loop Drive is a 142 miles long figure eight road, that goes the distance around the park displaying beautiful nature. The beginning and end of the road is at Mammoth Hot Springs. Drive this loop and stop many of Yellowstone's most famous attractions.
Especially if you are on limited time ( 1 or 2 days), you may have to choose between the Upper and Lower Loops of the Figure Eight. Total driving distance is about 140 miles If you have more time, try to drive it all before you leave because it really demonstrates the variety of natural wonders that is Yellowstone. This road was also constructed to bring you close, by car to some of the Park's most impressive sights. There are many scenic viewpoints and pullouts along the road. From the geysers and hot springs in the geyser basins in the West, wild life viewing in Hayden Valley to the still expanse of the caldera Yellowstone Lake and the spectacular upper and lower falls along the Grand Canyon of the Yellowstone, this road really takes you places.
The downside is that the road can be very crowded and there can be slow traffic and lots of rubber-necking (especially if there is wildlife around) in the peak months of July and August. If its an option, I would come in June or September instead.