The first ride I did was the Vishnu Overlook Loop. First I misread the instructions and ended up on a nature walk--nice for a nature walk but a boring mountain bike ride.
Then I decided to climb the tower:
It had two good consequences: nice views, and I discovered the real mountain-bike trail started just underneath the tower. Here are some of the nice views:
I had a nice short 1.5 ride on single track, with a nice bench and views at the turn-around point.
A few days later I rode the Tusayan loops. I should have stuck to loop 1 as it is shorter and I suspect had more single-track. I did loop 2 because I wanted something longer. It was about 10 miles long, but not terribly interesting and I was wishing I were at the Grand Canyon seeing the magnificent views. So scratch that from the plans next time. But one nice thing is I was all alone and it was peaceful. You don't get much alone-time at the Grand Canyon.
Here's the start of this trail:
On it's own, it's actually pretty and nice and there are some fun spots. I think the shorter loop would be better so I can have some fun, but then get to the Grand Canyon to see the great scenes.