In Sydney, rather than staying in the CBD, I recommend Coogee. It's only a short journey from the Opera House, costing around £15 in an Uber, but it's an absolutely gorgeous beach town, with lots of dining options. We stayed at the Coogee Sands Hotel and Apartments, in a Deluxe Oceanview Terrace Room - room 416. It had an enormous terrace with sun loungers and a big table with seating for 6. It overlooks the ocean and the Pavilion. Absolutely brilliant if you fancy a night on the balcony with a take-away. Would be great if kids were tired.
Don't miss having a meal at the Opera Bar. It's at the base of the Opera House and the setting is stunning. The fish and chips are lovely! The kids might enjoy seeing the dogs that are on patrol to scare away the seagulls! You can take a boat here over to Manly, which is really enjoyable.
Don't expect to see many Kangaroos. To seek them out, find a golf course. Don't worry about spiders, we only saw one tiny one in 3 weeks.
Painsville is a lovely little town. We stayed at Mariners Cove which is literally on the water. If you want to see Koala's go to Raymond Island. You get a 5 minute ferry there which is fun. If you want to eat at the restaurant that sits on the water, book in advance.
I echo a PP who recommended the Jen Singapore Orchard Gateway in Singapore. If you book a Club Room here, you will have access to the Executive Lounge on the top floor. You can get a quiet breakfast in here (away from the main restaurant), also at night you can get food here (hot and cold) and also alcoholic drinks for 2 hours, all for FREE. Children are allowed in here. As it's rooftop, you get amazing vistas across the City and you can see the Marina Bay Sands all lit up. You can also swim at night. There's a Tiki Bar at the pool. You can get a lift right down into the Metro too. Stunning hotel!
I'm sure the kids would love the Duck Tours in Singapore. They are boats that can also be driven on land. You start off on land, tour around the streets, then plunge into the water and sail around the harbour. Fantastic fun! You MUST book ahead to get a place, it's very popular.
The Merlion is great to see. There is a Universal theme park here too, if that's your bag.