Ah yes, I hiked the Delicate Arch hike, too. It would be a great family hike, since it is so short. It was special for me, because it is one of the four pictures on my bank checks.
My group also saw several bighorn sheep, but much farther away. One was in the bowl below, others were barely visible half a mile or so in the distance.
We went in the afternoon, and watched the sunset from the end of the trail. There were several hundred people there, but due to the beauty of the spot, there was quite a hushed, reverent mood.
Definitely a good nomination.