There was a great story in the Pittsburgh news this week. Two young kids saw a parrot flying around their neighborhood, and were able to entice it down from the trees (using a grape as bait). They brought it into the house, and then started tracking down the owner.
At the same time, a frantic owner was doing all the right things. They posted pictures and flyers everywhere, called the local police, etc.

Four days after the Senegal parrot escaped, he was reunited with his family thanks to a flyer posted at a local health club. It turns out he was still within a mile or so if his home the whole time.
There was a great story in the Pittsburgh news this week. Two young kids saw a parrot flying around their ... local health club. It turns out he was still within a mile or so if his home the whole time.

Just from anecdotal experience that seems to be the usual case. In most bird rescue stories I've read about, the birds were found not far from their owner's home.
Rick