Usually a deer won't be more than 2-3 miles from his home territory and even less if there's ample does around. A buck could travel like 7 miles or more in a day chasin' does, but that includes going in circles, doubling back, criss-crossing, etc.
During the rut I wouldn't try to hunt one buck due to his chasing... unless I know of a single buck that is a definite shooter and believe I know where he beds, then I may go for him.
iSnipe