Go abroad and you'll hear news of home information about one's immediate vicinity may have become more widely publicized at a distance; saying recorded from the late 17th century.
go further and fare worse it is often wise to take what is on offer; proverbial saying, mid 16th century.
go the extra mile make an extra effort, do more than is strictly asked or required. In a revue song (1957) by Joyce Grenfell, but perhaps ultimately in allusion to Matthew 5:41 ‘And whosoever shall compel thee to go a mile, go with him twain.’
See also go to the country, go the distance, goes, go to the mat, go to town.