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.
Beach approachable by public transportation and can be connected with a visit of MOMA PS1 Art Installation (Katharina Grosse House) Also less crowed than other beaches in NYC.
From Wally's cafe to Wall.E to a green wall. When you arrive in NYC you immediately mention a difference in concentration when it comes to conversations. Iphone's go always before listening to people. There is nothing to do anything about this anymore but it is a little fact.
I Like to cycle and walk around in the neighborhood and mention this beautiful wall with the 2 oval light spots arisen on it. This magical light spots are constantly popp'n up on all different walls in NYC. Open your eyes: Let's stare at the wall. Just as long as something starts happening.