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.
This quaint shop boasts an artfully arranged and tastefully curated selection of jewelry, pottery, books and art. I have to keep myself from going there too often, because I have trouble leaving without making a purchase.
The best underground shows you will find will have free pbr and models as far as the eye can see. They are rarely announced, so keep your eyes out for promising openings, especially with Milk Underground coming up.