Some good books to help you learn about New York City:

This absolutely beautiful book will enhance your experience and make it last a lifetime.
The Historical Atlas of New York City

The Blue Guide is chock full of all sorts of useful information running the gamut from restaurants and transportation to history. Highly recommended.
The Blue Guide

Not extensive but condensed -- a good one to carry with you on your trip
Frommers 2009

This book provides extensive information on many of the city's 20,000 interior, exterior, and scenic landmarks.
Guide to New York City Landmarks

Detailed information on one of the city's most prominent landmarks
The Empire State Building

For kids
Storied City

For bibliophiles
Literary Landmarks of New York City

For clubbers (a lot of good info but missing some of the hippest stuff, frankly)
ZAGAT Guide to Nightlife

New York is notoriously expensive, but there's a ton of stuff to do free and cheap while you're here.
NYC Free & Dirt Cheap

Another good one for economizers
The Cheap Bastard's Guide to New York City

Of course, even if you read all of the above books, you'll still need a guide for at least a few hours!