I'm not fully sure, really.

Because she didn't know where to go to see the lights. She needed a guide to take her there because she intended to go back home.

I think she would have taken her chance eventually. Flynn was just an opportunity. But she would have one day simple went and marched in the general direction until she found help.

She clearly had planned it before Flynn.

I think she would have found a way, once she was determined to have her way. she just preferred to do it with a guide because it sounded safer and with someone who actually DOES know the way, it would go much faster.

I don't know if should would ever find the courage to honestly. Her entire life her mother's been filling her head with propaganda about how monstrous men are and how dangerous the world is. It's only when she meets Eugene that she realizes her mother's been lying to her, and that's what prompts her to go against her mothers wishes and see the lights. Without Eugene acting as catalyst, I don't know if Rapunzel would have ever found the courage to leave. In fact, after a few years of asking, she might stop wishing for it all together. Especially if Gothel is able to instill enough fear into her over the years.

What opportunity would she have? None. She'd get lost and probably die since she has no survival skills minus the magical hair. By then Gothel would find her and bring her back.

To be honest I think she would have found a reason to leave eventually.

Probably next year.