Beaver Run is a good, established neighborhood. Very safe, in Midland, but not too far from downtown Columbus. Mathews elementary, Midland Middle, are very good schools, rated 8 or above in great school.net.
We have several wonderful neighborhoods in Columbus. Many are "tucked away" without crazy traffic and noise. Some of the more popular, upscale neighborhoods are are Green Island Hills, Brookstone, Sears Woods, and Hilton. If you are looking in the the range of $150's to $200's there is Windsor Park, Lakebottom. Garrett Creek and Mohina Woods.