I've discovered the first and I think the only free eats in Battery Park. They hail from Inatteso, the brand new Italian cafe on the ground floor of the Millennium Tower (3o West Street). The Casano family [of Adrienne's Pizzabar, Harry's Steakhouse and Ulysses] owns and operates both the cafe and the recently opened Inatteso Pizzabar Casano, where I once devoured an entire Grandma style brick-oven pie topped with broccoli rabe and sausage (in my fatter, paying days).
So what's for free? Well since the cafe is still new, they've been sampling a variety of stuff to familiarize their neighbors with the local goods...like Italian cheeses imported from Brooklyn, and homemade signature desserts that have that "straight out of Sicily" deliciousness. While the Nutella cake will cost you $5 a slice, it's rich and worth a try. For something more budget-friendly, ask for their chocolate chip cookie. It's quickly becoming one of the most-talked-about cookies in Battery Park and I can attest, it's got more chocolate chunks per square inch than any cookies I've seen South of the border (Canal Street). I recommend having all of the Inatteso sweets (free or purchased) with a strong cup of Lavazza espresso, served fresh in adorable espresso-sized takeaway cups. A small detail I always take issue with at Starbucks where I'm usually served [burnt] espresso in a grande cup. So unsatisfying.