I walk on whichever damn side I feel like walkin' on, see? And if I see you, you better cross over to the other one!

Anyways, there ain't no wrong side to a sidewalk unless ya mean the underside of it, and you can't walk a dog there. The only thing you might do on the underside of the sidewalk is dig up Jimmy Hoffa, providin' you dug in exactly the right place.