I live above TriBeCa and take walks into and around this area often. It's quiet, usually on the emptier side, and hosts a few gems of restaurants including Tiny's, Takahachi, and Odeon - all on the same block of West Broadway.
Have you ever had Uzbek food? Me neither until I went to Nargis Cafe. It's kinda like middle eastern food mixed with Ukranian food. It's so good and so inexpensive.
My second-favorite outdoor-place in Manhattan. The abandoned 1.6 km rail tracks running above Chelsea down to the Meatpacking district were turned into an above-ground park. Perfectly nice place for sitting in the sun, reading, relaxing, having lunch in some green spot in the city. Nice views at the Hudson River, New Jersey, the Statue of Liberty (little small from there but still visible) and the architecture around Chelsea.
I feel like I've watched this plant shop grow up because they've over doubled in size since I first started going! Speaks to the quality of the store and ownership. They have an excellent selection of healthy plants for a great value. This is my go to for green.