Well, I think Mountain Brook is probably the school system for you. We're not Jewish, but I believe somewhere around 20%-25% of the school system is. So you see interesting things such as no homework during Yom Kippur, etc. etc. Plus my two older children, being adolescents, have attended a lot of Bar and Bat Mitzvahs (sp?).
Also, an interesting development is the recent construction of two temples on Overton Road section of Mountain Brook in the 35223 zip code. The reason for the new temples is that the old neighborhoods had become so pricey that it was next to impossible for young couples to buy a home and walk to temple on Sabbath. One is Reform and the other is Orthodox, about 500 yards from one another. So on Friday nights and Saturdays, you see a lot of Jewish folk walking to their respective temples.
Also, there's the very good Jewish Community Center on Montclair Road, which is an excellent recreation center, with pool, daycare program, fitness facilities and the whatnot. Actually, given that we're members, it's pretty popular with the non-Jewish population, too. In fact, my wife and I joke that it should be called the Jewish-Episcopal Community Center, given how many members of my church belong.
The area on Overton Road is a pretty affordable area of Mountain Brook, plus it abuts the Cahaba Heights section of Vestavia Hills. Both are extremely convenient sections of town for shopping and the like, yet close enough into town to make a reasonably short commute. What's more, in this market, I think there are a few rental houses in the area. You should go to
al.com - Everything Alabama, the Birmingham News' web site to check out their classifieds. That should give you an idea about rentals.
You are right about the Birmingham City schools. They are terrible. We wound up sending all three of our kids to private schools when we lived in Birmingham's Forest Park section (Great part of town, by the way). However, Mountain Brook is rated one of the top twenty public school systems in the country by some organization. We've been very pleased with the education and environment there. You would also do well with Homewood, Vestavia, and Hoover--Although Hoover would mean a longer commute.
I hope that this information is helpful, particularly concerning the Jewish community. I can only go by what my Jewish friends tell me.
Good luck in your search.