There are some lovely family friendly properties at the Kennedy Road end of Mid-Levels, but the starting price is nearer $60k and more if you want a good sized apartment in decent condition.
Grand Promenade at Taikoo is family friendly and closer to your budget. It's very convenient for Quarry Bay promenade which is great for kids to use their scooters and bikes. Happy Valley is full of expat families and should suitable places in your price range. I have quite a few friends who live there and they love it.
And don't forget that taxis are very cheap and convenient here.