School is indeed tricky in Hong Kong, but I am sure you will find a way to figure that out
Not exactly Kwun Tong, but try The Wings at Tseung Kwan O. It has a really nice shared area including swimming pool, gym, kids playground, etc. It is on top of a shopping mall and the MTR which can bring you anywhere close in about 30-45 minutes. Not if you want to travel to the Outlying Islands though.
Clearwater Bay and Sai Kung are really nice, but the traffic can be horrendous at times, especially during the summer months on Hiram Highway. There is no MTR there, so you will have to rely on public transport or own transport.
Furthermore, I think it depends on where your office is. Otherwise you might consider Pokfulam, Kennedy Town, Happy Valley. All really cool areas and close to good schools