I'm an asperger's too and have tons of excess energy. What I've been doing is going to the gym daily and working myself ragged with the goal of training in martial arts. I 3rd the martial arts idea, because even though they do have classes, it's a great sport to do alone too, get yourself a bag to kick or something, do some moves, meditate. Another thing I was looking into myself was archery. Yes, the equip might start out as expensive and in some places, ranges might be far away. So, I don't know about your situation. Where I'm at (Columbus, a city of course) doesn't have much in regards to archery, but there are places / clubs you can join to shoot alone.
So, archery and martial arts. Golf can be done alone. Shoot some! It's unfortunate all these things cost money..... go on hike trails? I like to pretend I'm on an adventure and go walking for hours..