If you're looking for a place to unwind after a busy day exploring, then you can't go wrong.
Vaucluse is absolutely stunning. The little beaches are beautiful, with Watson's Bay ferry less than 10mins walk away (for little feet).
Be aware though if you don't have a car, although the buses are convenient, grocery shopping is very limited if you're on a budget!
There is a corner shop that sells essentials, but the nearest Coles is a 25min bus ride away, and it's not cheap - if buying groceries for the family on a budget, you're better off catching the ferry across to Manly and hitting the Aldi on the wharf.
The apartment is lovely - it is on the second floor with its own private courtyard. The house is lived in, so there are bits and pieces locked away understandably, and the hosts make a good effort in making you feel at home.