Where can I travel close to NYC?

I’m visiting NYC from Australia and have 1 week to explore areas outside NYC, before I have to return to NYC, I was wondering what’s close by or east to get to on train or bus. I’m hesitant to rent a car considering I’ll be on the opposite site of the road!

I’ll be alone as a young woman, so something relatively safe to do alone - I’d love to go somewhere in nature with hikes etc, but quite open to options.