Understand that bighorn sheep live in various places scattered around Yellowstone, but there is one location where your chance of seeing a bighorn—and usually more than just one—is excellent.
Go to the short road that leads from Mammoth Hot Springs to the north entrance to the park. A couple of miles from Mammoth, this road will enter a deep canyon cut by the Gardner River.
Look to your right, if you are headed north (to the east, that is). Along the edges of the high cliffs you will see here, look for sheep.
Look especially along the top of the cliffs, where the sheep will be silhouetted against the sky. Watch out: the sheep kick rocks loose sometimes.
Look for people gathered in the turnouts. Look especially for large groups composed of people looking almost straight up, with binoculars and spotting scopes. This trick will often lead you to wildlife in Yellowstone.