I would've gone the opposite way- to the havens.
After my own lobbying efforts failed, that is. I would've pushed for someone to wield the ring against Sauron, and when it became clear that no one would do such a thing, I might've tried to steal the thing in order to keep it from being sent straight to Sauron. (I wouldn't have seen any hope whatsoever in the plan to send Frodo to Mt. Doom. I mean really- what are the odds Sauron doesn't post a battalion of guards right in the Cracks of Doom seeing how important it is.
)
So yeah- I would've been a version of Boromir. But if I wasn't able to get a chance to steal it or was unsuccessful, I would've gone straight in the opposite direction and hope I could get across the sea before Sauron got his ring and flattened everyone.