If you are not into city stays, I would highly recommend Felicia's place (18 mins by car from Melbourne CBD).
We spent 12 days at her beautiful home and enjoyed every moment of it. We had a "home" (away from home) with good space, great morning sunlight and a nice little courtyard. Restaurants and supermarkets are just a few minutes drive away.
Felicia was also an excellent host checking in on us from time to time to see if we were settling in well.
I would highly recommend her place for a small family who are looking to stay out of the CBD area.