I would suggest this place, right off the West Side Highway, and right on the bike path:
http://www.pier40parking.com/
If you definitely want to be close to Battery Park, some of the garages in Battery Park City would be easiest. I can get a specific address for you later in the week, as I bike over there all the time. PM me if you want; I live in the Financial District and can easily check out whatever you need.
It's usually possible to park on the street on weekends, but you might have to drive around hunting a space.
Pam



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