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.
Spoonbill and Sugartown Booksellers is in a pretty visible spot at 218 Bedford Avenue in the Williamsburg neighborhood. I still can’t help but point it out as one of my favorite places to check out books, especially arts related publications. Needless to say its an easy place to stop by with plenty of things to see in the immediate area.
After the full moon, when the tide is the lowest, you'll find a century of fossils from a gone NY, trails of washed-out rainbow colored bottles, a graffitied shipwreck buried by time. Hundreds of years of history written in the sand.
Giant dinosaurs. And the rest of the museum is great if you also like giant whales and outer space and especially the life size dioramas of animals and cave people, which might be the very best Art in all of the city. Sigh.