Greenwich St, Tribeca

The corner of Greenwich and Canal has some really cool buildings. One is a new, condo building with stunning units, one is a federal row house, and the other is a cast iron commercial space. It's a really interesting showcase of the evolution of New York architecture. Across Watts, there are more historical buildings, but they have always been commercial spaces. Commercial spots as historical landmarks aren't all that common in this area, so they're definitely worth a look.
As you go further down Greenwich, a definite theme is established with commercial buildings on the west side and apartment building with little bars and restaurants on the ground floor on the east side. The must-do of this stretch is at Moore. The Tribeca Film center is right on the corner with a few restaurants surrounding it that are all fantastic. This is a very trendy little corner and I always recommend that people take a peek.
This street, around Moore, is a great street to live on because the apartment buildings are fantastic (though very expensive), the restaurant scene is great, and Greenwich is far enough west that there isn't a lot in the way of traffic, tourists and lurkers. So, it's a bit quieter than a lot of other streets in the neighborhood. I like Greenwich street in its entirety, and the Tribeca stretch is no exception. It's a really cool street.