St Mary's Cathedral is a Catholic Church in the heart of Sydney's CBD. You can find it across the road from Hyde Park, or exiting the Royal Botanic Gardens towards Town Hall station. Even if you're not Catholic or Christian, it's still worth visiting to admire the architecture, and you are welcome to take pictures - just be respectful and try not to disturb those praying or attending Mass. The outside depicts Gothic Revival architecture, made from Sydney sandstone. It's an even more awe-inspiring spectacle inside, with stained glass windows and marble flooring.
The cathedral is a quiet place for prayer, meditation and reflection, with many shrines set up throughout the church. It's also a popular place for weddings, so look out for signs as you may not be allowed in or allowed to take pictures during the ceremony. Mass runs daily throughout the week, even during lunchtime at 1:10pm to serve the busy city workers. They also have Mass at the usual times on the weekend (9am, 10:30am, etc.). Check their website to confirm.