Welcome to Cleveland, Beehn!
Northeast Ohio has several wonderful family communities. I've lived here most of my life and my wife and I are currently raising a 2 year-old in Twinsburg (about 20 miles south of C-town). What type of community are you looking for? Northeast Ohio communities run the gamut from chic & urban to quaint & historic and everything in between. The "ring" of suburbs around Cleveland is not as extensive as many other "large" US cities. In other words, there aren't endless miles & miles of suburbs (like in Chicago). Rather, there are one or two "layers" of suburbs and then smaller townships, villages & farming communities. So you can basically get from downtown to a small farming community in 30-45 minutes. If you let me know exactly what type of community you're looking for, I can help steer you in the right direction.
In the meantime - every year, Cleveland Magazine puts out an extensive report ranking the top 50 Cleveland suburbs (the rankings take into account EVERYTHING - including school systems, safety, services, taxes, park systems, recreation & entertainment, etc.). The rankings are designed to highlight which suburbs offer the best bang for your buck (i.e. the "value" of the community when considering all factors). In other words, it doesn't necessarily list the suburbs in order of "most desirable" - case in point - I know many NE Ohioans who would move to Chagrin Falls if money were no object. Yet, because of its cost of living (and probably also due to it's lack of diversity), it's only #20 on this list...
Did a quick google search - here are the top 20 from the 2007 rankings:
1)Solon
2)Moreland Hills
3)Mayfield Village
4)Avon Lake
5)Twinsburg
6)Pepper Pike
7)Highland Heights
8)Orange Village
9)Brecksville
10)Independence
11)Chardon
12)Chester Township
13)Aurora
14)Avon
15)Kirtland
16)Beachwood
17)Concord Township
18)Rocky River
19)Westlake
20)Chagrin Falls