Agree with the other posts. For work, lots of offices in Hawthorn and Camberwell and then along Canterbury Rd out to Blackburn in terms of work. Richmond also is the next suburb with variety of work potentially. For kids, if they are sporty then again Camberwell, Balwyn, Kew, Richmond and Hawthorn all have clubs of anything you might want and lots of fields/parks/sporting arenas to cater to them. Very good private and public schools in the area (most public are tight on their zones because they are so good and able to be selective if you are not in the catchment zone). Suggest somewhere near the train/tram line or bus route so kids can get around to their activities and friends. Really depends on your budget.
I lived in Canterbury for a while, very expensive for what you get, don't expect much of a backyard. Nearby though good value in Balwyn, Balwyn North, Mont Albert and Surry Hills. There are pockets of North Balwyn on the Northern side of Doncaster Rd which I really like. How far do you want to drive each day?
You're spoilt for choice if you can afford it. In terms of work and living, Camberwell is pretty good for professional, retail, office or hospitality jobs. Richmond and Kew are also hubs close to the city. If you'd consider a bit further out, Box Hill is also good. Of these suburbs, Box Hill's probably the cheapest and still children-friendly. Like Camberwell, Richmond and Kew, there's considerable parkland and bike tracks, and it's still within cooee of reputable schools.
Really depends on your budget as this area and surrounding is some of the most expensive areas in Melbourne - but there are great schools in the area. I think the pick of the nearby suburbs for kids is Kew & Canterbury (huge dollars). I'd then look at Camberwell, Balwyn and Hawthorn itself (ever so slightly cheaper, but still very expensive).