I live in family friendly Chorlton, its not the be all and end all, but there are a large number of primary schools to choose from, there are beautiful parks, and its all very child friendly.
Oh, and we just 3 tram stations...takes you into town in about 15 minutes. Awesome. Forget busses, we've got shiny new beautiful trams.
Didsbury is also family friendly, I don't find Fallowfield to be nearly as family friendly, mainly because of the large student population. I live in an area called Firswood, and there are a number of houses there for rent, mainly 3 bedroom semi detatched properties, I live a block away from the tram station, within walking distance of about 6 primary schools, two sure start centres, baby/playgroups every day of the week, a small supermarket, lots of local shopping and an amazing vegan fairtrade organic cooperative grocery store. You could be at the University on the 86 bus in 20 minutes, the busses are really frequent. One nice thing about Firswood is that we straddle two councils, so you can use the facilities of both Trafford & Manchester. Anywhoo...I am babbling now, feel free to PM me with any questions etc.