The draw is the ability to walk a loop trail into Monument Valley around one of the Mittens without requiring the services of a Navajo guide. Being able to get so close to one of those 1500ft behemoths gives a different perspective than viewing from The View hotel.
When facing The View from the parking lot, Wildcat Trail is off to the left where the campground is located. It's a 3.2 mile, self-guided loop that takes you around the West Mitten Butte.
If you're hiking during the summer be sure to go early and bring a lot of water. You're fully exposed on the trail, and even though it's short it's easy to underestimate the desert heat.
I hiked during the winter. I definitely recommend a heavier jacket due to the cold temperature and wind chill.
The trail offers a different perspective of Monument Valley than you can get on the 7 mile car loop.