It looks good to me. My only concern would be the slats of the fence are far enough apart that people from the outside can look in and maybe see them. I'm paranoid about mine being stolen, so that would bug me. Other than that - it looks nice!
The tree is a live oak. I am leaning toward the corner location too, and incorporating the whole area eventually.
you can't see in through the fence, our neighborhood is tortoise friendly We have gopher tortoise burrow with a gopher living in it, and my kids found a baby gopher tortoise out in front of our house.
So now onto raking and clearing the area. Still not sure what kid of border to put around the edge.
I use 1x12 boards as the border. You'll need to incororate a water structure. I put seating boards on the corners prevent climbing and furnish shady resting places for the torts. It looks like a very good location. By the by, I'm jealous, you have a resident gopher tort.