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.
Arthur Avenue is a mainstay of the Bronx. Since the early 1900's til today, it's been the hub of the Italian-American community that calls the Bronx home. Many family-owned, traditional businesses dot the main avenue, and the food culture is rich and boisterous.
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.