Parking for Mineola LIRR station?

I am interested in moving to a house in the general area of the Mineola LIRR but it's not actually in Mineola. The closest train station is East Williston, but that train line isn't nearly as good as the Mineola train.

So I am interested in using the Mineola train station. Is there a good place for non-Mineola residents to park? I'm interested whether or not I have to pay for it. And for what it's worth, I would be taking trains around or shortly before 7 AM.

Thanks for any help.