Thanks for all of the responses! This forum is fantastic.
MTS: We currently live on the upper east side in the midst of the richest blocks of Manhattan (happens to be the location of the married-people-housing provided by my wife's school). We don't expect to find a Cleveland-equivalent. I would prefer to rent for a year or so after moving to Ohio, to become more familiar with all of the options, but I'm not sure if this will be possible-- my wife is anxious to buy a house as soon as possible. (hence, why I am turning to this forum!).
CleveChiNola: thanks for the recommendation, but the "Intervene Rational" School seems a bit too experimental for our future and hypothetical children. :)
joerunnin13: from the time we spent there, and based on my wife's online real estate research, I was getting a similar feeling about Tremont. There doesn't seem to be as many solid, several-roomed houses that a family can grow into. But if somebody else has contrary information, I'm all ears, because we love it there.
I appreciate the Lakewood recommendations, but my wife would be working in university circle and I'd probably also work there or elsewhere on the east side. We want to minimize commuting time to some extent, meaning Detroit-Shoreway is the furthest west we'd go. We'd also like a single-family house that could potentially be for the long-term (we hope to have several children). We are probably not cut out to be true urban pioneers-- we need to find a neighborhood with other families that feels safe, and is safe.
I realize Cleveland Heights is probably the obvious choice (right?). But we're exploring these other neighborhoods because (i) we've loved Tremont the few times we've visited, (ii) we are active in our church, and there are excellent churches in Tremont and Detroit-Shoreway that would be great to live near, and (iii) I grew up in a west-side suburb so it is difficult for me to imagine living on the east side with all of those east-siders. (joking).
Thanks again for all of the information so far.