When visiting Sydney the temptation is to stay in the Rocks (the district the world thinks of as Sydney). Don't, it's a tourist trap. Instead, consider Kings Cross or Darlinghurst. These districts are the heart of Sydney. Not as pretty but much more fun.
If you're just in Mumbai for the day, passing through, stay at the Leela. It's a good five-star hotel two minutes from the international airport. Mumbai is a fantastic city but traffic can be a problem so if you don't have to journey into her, don't.
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