What constituted a "higher standard of living" for us was a short commute, walkable area, cultural activities near our house, diversity in every sense of the word, and an area with a sense of community.
For raising our daughter, we balanced the quality of public schools with the education received by being around different people from different walks of life. Our goal as parents is to raise not only a reasonably intelligent child, but one who can understand and empathize with people different from her.
Btw, despite being < 1 mile from what would be considered the inner city, we have very little crime. I think this is due in part to neighbors all being close. We know when someone is out of town and what work schedules are. We also have a decent contingent of people who work from home. Add to that my own impression, from being raised in a poor working class area, that inner city crime certainly exists but has taken on a boogie-man hype factor.