I lived in Chiswick for a year and a half until July there. It's a nice enough area but there is literally nothing there beside the apartment complex except for a convenience store and an Italian restaurant, albeit a very good one. There are frequent buses and ferries to the city if you want to go for a night out but it gets old after a while.
As already mentioned check out Rozelle/Balmain, Glebe, Neutral Bay. Northern beaches may be worth a look too, Manly etc?