We went in May and to be honest, there really aren't any good areas to run. It's my favorite resort but least favorite to run.
I got excited when I heard there was a trail between Jambo House and Kidani Village but it's basically a sidewalk that's about half a mile.
I ended up running back and forth between the resorts in the parking lots. You can circle the back areas of the lots and don't have to worry about cars but you definitely won't see anything of interest.
If you have a car, I recommend driving over to the Boardwalk area and jogging there.
I was there last week, and i asked the bell man and the front desk about running, they told me there is no place to run other than the tredmil. very disappointing
AKL didn't have any decent place for an outside run, but the treadmills weren't so bad. I just cut my mileage down, and sped up a bit, and went with that. It's a pity - I'd love to run around outside at AKL; it's such a great resort.