I've oddly, been sort of the exact opposite, and sort of seek out high places. For instance, I enjoy going to the top of skyscrapers and looking out at the skyline. I also enjoy crossing high bridges that allow me to see for miles. I've always like sitting above a crowd, looking over everyone's head. As a kid, I loved climbing trees and getting several feet above the ground. My parents had a maple tree in the front yard I could get over the roofline of the house in. To me, you're not high enough till you break the treeline, and can see above the trees.
I only get skiddish of heights when the supporting structure is a little flimsy. My job entails climbing ladders, and I generally have no problem going up the standard 6 or 8 foot "A" style ladders to do work in suspended ceilings or something. I do get a little squeamish though when I need to climb tall, shakey scaffolding or other structures that shake and jitter. When it comes to heights, I ususally like to use the "Genie" lifts which are a platform that goes up and down like an elevator. While they shake around a little bit with your movement, there's usually little chance you're gonna come out the bucket unless you're reaching out too far or something.
I can't say that a fear of heights is an aspie trait, since I know of NT folks that are afraid to take 1 step off the ground!