Well.. There are a lot of of options in the area that are "child/family friendly". IMHO, Oxton is a bit far out from High School, but any of the "nicer areas" around the city would be ok.
As far as commuting goes, the easier areas are
West Bridgford (lots of alpha mummies, think wall to wall bugaboos and hummus)
Woodborough (Very "Villagey", but dont know it that well to comment)
Southwell (a bit far out, but lovely and villagey)
Gedling ( a little less "upmarket", but great schools and nice area)
Woodthorpe (GREAT schools, affordable and lots of shopping/parks)
Remember that the High school is kinda slightly north of the city centre, so commuting from south (like WB), means effectively crossing town twice each trip. Not a MASSIVE problem, but if you hate the car.... However, it IS also on the Tram Route from City-Hucknall, so that could be an option. Im guessing that you know that the girls school is private and (imho) pricey!
The commutes from Plumtree, WB, Wilford etc are all much of a muchness, but you WILL have to get into the city and out again. OR... You get to a tram station and wing it from there.
The commute from North/NE of city would be easier (sherwood/arnold/woodthorpe/redhill), but properties & facilities vary massively (all depends on budget really tbh)
In WB and surrounding, you will be knee deep in coffee mornings and kids facilities, but its just a bit TOO much for us (personal opinion). The same IS available everywhere else too, just maybe not the level of choice.