It would depend upon the circumstances. I would let my 13-14 year old daughter go to DisneyQuest for a couple of hours alone, since I know that she is extremely responsible. However, she would have to bring a 2 way radio with her, and I would check in with her at regular intervals.
I probably also would be in Downtown Disney at the time, enjoying the shops. While DisneyQuest is a self contained building, fairly easy to navigate, I wouldn't want her riding the buses to/from the resorts by herself - I don't even like riding the Downtown Disney bus!!
So - only you know the maturity level and capabilities of your 13 year old. My 13 year old daughter is 5 ft 9 in and looks like she is 18. Her best friend is tiny and looks to be about 9 years old. I would be leary of letting her friend be by herself in a public place - she is much more of a target.
That said, I have never let my girls go off by themselves - they can go off, but they have to stay together!!