1 night is not much and with 2 small kids the logistics of getting to/from the hotel is maybe dominant. Sydney has the most expensive hotels in the world, more expensive than London for example. For GBP 100 you get backpacker level accomodation (not quite, but you get the idea) and GBP 200 is probably the bare minimum and you will have to shop for a deal to get that price. August is mid-winter so the beaches accomodation will be cheaper, but not convenient or pleasant for you. I'd suggest one of the Circular Quay hotels (Intercontinental, Marriott, etc.) as a ferry trip is a must do. The Rocks is a peninsula on one side of circular quay and is the oldest part of sydney with some historic houses ... but also steep cobble-stone staired streets, so maybe not the best with small kids.