Although its first neighborhood was originally platted on an old farm in the 1910s, Upper Arlington has long since been engulfed and totally landlocked by Columbus. It is now several miles in all directions from UA, before you ever see any wide-open country
Within Arlington itself, there are properties that resemble country estates and have a pleasant, near-rural feel to them. But these usually come with $2-3MM price tags (or more)!
For an upscale area that's much more rural and close to the country itself, try Powell or New Albany. Or even Dublin.