My main form of exercise these days is walking. I'm very fond of being outdoors, with the sun on my skin (but not in my eyes). In fact, I think that walking may be one of the best possible ways to get exercise to begin with. A few reasons:
It's fun. Really, it is. You get to see the world around you and, if you like, lose yourself in the patterns of the leaves on the trees or the sand in the concrete. Or you can listen to a book on tape (highly recommended and probably available at Your Local Library; I'm just finishing the unabridged Lord of the Rings trilogy).
Experiencing, regularly, the sensation of movement is very important for people with touchy sensory systems and slightly out-of-whack proprioception. It's probably part of why many of us (autistic, sensory integration disorder, some ADHD, and quite a few dyspraxics) will tend to move our whole bodies in repetitive ways, such as rocking, spinning, or swinging. It helps us to get a sense of where we are in space. For those who are hypersensitive, the sensation of walking is rhythmic, regular, and comforting. For the hyposensitive, the same sensation works very much like stimming to help answer the "where am I, and how is my body moving?" question.
There's also the way we get better with practice at most things we do; and that includes walking. As a child, I couldn't kick or throw a ball with any kind of accuracy, and I couldn't run gracefully well into my early twenties. But for seven years, walking has been my most-used method of transportation (even with a car, I only drove outside of town; and I prefer walking to a bicycle for distances of two miles or less). All those years have paid off. I used to walk quite awkwardly. Even a couple of years ago, I would've just let my hands hang at my sides instead of using them to keep balance and rhythm; now, they swing in synch with my legs. Walking toes-down-first is another impulse that has been corrected over the time I've spent walking. While I still put my toes down first when I'm barefoot, I now put my heel down first when walking outside wearing shoes; this allows a longer stride.
I can run passably well now--not very fast and not very long, but at least not with the expectation of falling down after a few dozen steps. The more you do anything, the more coordinated you become at it; and walking or running is a skill that anyone who is not too graceful should practice. You never know when you'll be stranded and have to use your own two legs to get out of a situation.
And, of course, walking is useful. You can get from Point A to Point B without having anybody cart you around, without having to get out the car or the bicycle, and without having to deal with traffic except while crossing streets.
There are a few drawbacks to walking, though.
First of all, you've got to wear shoes. I know--many of us don't like shoes. They're constricting, they squish your toes, and you have to tie the laces. But really, pick a good pair, and it's not that bad. You don't have to get anything that expensive; in fact, I suggest you don't. High-performance runners may need expensive footwear, but for simple walking, there's no need to worry about anything beyond whether the shoe feels good on your foot and whether you get decent support (I tend toward weak ankles, and this is one of the things I look for when I buy shoes.) Oddly enough, the sole is more important for ankle support than the top of the shoe. Look for a nice, broad sole that doesn't tip over when you put more weight on one side of the shoe than the other (and believe me, if you are the least bit clumsy, you will. Probably while tripping over thin air.) Get Velcro closures if you hate laces; or just tie the laces loosely enough to slip the shoe onto your foot without untying them.
Second: The sensory issues. With walking, there are a few sensory issues to be aware of: You'll probably sweat somewhat (unless you're in very good shape), and that sensation can be annoying. There's wind, which some people like (I personally do), sun, and temperature extremes. Sweat doesn't pose that much of a problem in lower humidity and temperate weather; but in high humidity, or in cold weather when you have to bundle up, it can stay on your skin and feel awful. There are shirts made of material that is supposed to keep you relatively dry; and they do help (girls, sports bras can be made of similar material); but of course there's the question of whether the material feels worse than being damp would feel. Sun in your eyes is an easy problem to solve; just wear sunglasses. Temperature extremes can be dealt with by wearing decent clothing. If you are going out for longer than a half hour, bring a bottle of water; longer than two hours or in the heat, bring more water (or know where to get some; for example, if I am walking to the library, I only take one bottle of water and refill it at their water fountain).
Third: You're autistic and you're out in public. That can be an issue even if you're totally independent, because, let's face it, we look odd enough to make most cops look twice. You may choose to memorize a standard procedure for dealing with police officers. If you don't trust yourself to be able to explain things, you can wear a MedicAlert bracelet or necklace, or carry a card in your wallet that explains the problem. For people who aren't police officers, the best thing is just to look as though you're not a good target, and to stay out of areas where people might target you. (Areas where the buildings are in good repair tend to be safer.) People with upright posture, who move quickly, seem to be targeted less.
Carry a nonlethal weapon in case you are attacked (I carry pepper spray). Why nonlethal? Because you won't hesitate to use it. It's no good worrying about whether your judgment is good enough to tell whether a fellow intends to mug you or not; better to find a weapon you won't wait too long to use. Of course, your first line of defense, beyond staying out of bad areas to begin with, is simply running in the other direction; the weapon is for if you're cornered. Even if you do have to mace somebody, the next step would still be to run. (See why I think learning coordination is important?)
The nice thing about walking is that it's something most people can do, doesn't require any kind of special equipment that you probably don't have already, and is just plain useful. And yes, you do get an endorphin rush from walking. It's the exact same thing as the "runner's high", only you don't have to half-kill yourself to feel it.