I live in the city limits but there is a wooded area near where I live too. A few years ago, we noticed a pair of coyotes a couple of times...then a few years ago, there was only one. It travels on a little wildlife trail (made by whatever animals go back and forth on the back of our property to the adjoining drainage ditch where there is water.) The last time I saw it was right after my last son was born a couple of years ago. I recently saw it again. I was able to run out onto the porch and take a picture of it from afar. It trots fast only at the back of the yard and goes to wherever it lives in the woods, never into our yard or around us.
We used to visit a relative who lived in a rural county hours away from us. The coyotes there ate the livestock and were a menace. When one was killed, whoever killed it would hang it upside down on their wooden fence so that everyone else could see (as I assume it was their common practice to show that there is one less coyote out there.)
I don't normally see much wildlife like deer or coyotes where I live, but when I do, it's wonderful...
edit to add:
Check out Melody at SOOC (Straight Out of the Camera)