When you don't have all your wedding luggage with you, we'd recommend taking the ferry from Sydney's Circular Quay to Manly. It's a short 15-20 minute ride but you get the most amazing views of the Opera House, the Harbour Bridge, the harbour, and Sydney's North Head (a headland). Manly is a really nice (if a little touristy) area with shopping, beaches, and amazing food.
If you like zoos, Taronga is a great one. It's a short ferry ride or bus ride from Sydney's CBD, has a huge array of native and international animals (you're guaranteed to see a real life kangaroo) and you can even book a meet and greet with a koala. Plus the giraffe exhibit boasts some of the best views of the Sydney Harbour in the entire city. If you're REALLY looking for something wild, they also have a hotel IN the zoo so you can stay overnight. I think there's a nocturnal tour for hotel guests too.