how to go to Blue Mountain

Hello! We are bound to Sydney in couple weeks and Blue Mountain is in my itinerary. I'm debating whether to go on package tour or just do it ourselves. What is the best way to take by public transportation from the city. Is it worth it or do you suggest just doing a package tour? Thanks for your input. Any other cool things we can do, we're only going to be there for 4 days.

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