The first time I went to a reading at the Union Square Barnes and Noble, I was amazing by a couple of things. First, the huge size of the store, second, the amount of people it could hold, and three, that they had such a problem with crowd control that they needed to place instructional stickers (see above) on each and every chair that was set up at a reading. The truth is, the Union Square Barnes and Noble doesn't host readings, it hosts celebrity sightings. If you want something with a little more depth, you'll mostly have to go elsewhere.
Since reading series come and go in the City like rats in the West 4th Street Subway Station, the best way to find a good series is by searching out the venues themselves. For example, the Bowery Poetry Club and Cafe, (308 Bowery) almost always has something interesting and semi-literary or at least semi-literate going on, sometimes more than one thing in any given night. They often have storytelling events as well. Stay away from anything marked “Slam” unless you are up for a very specific type of experience, since those are often open access, open mic type events. Any given performer might be fantastic but they also might be horrendous. Bowery has a bar, and while events usually have a cover, there is seldom a drink minimum.
Another place to look is the Housing Works Cafe, one of the best bookstores in town. Housing Works hosts all sorts of different readings, and events; as of this writing they had a “speed shrinking” event scheduled, where troubled New Yorkers could meet and greet a number of therapists in a short period of time. Ah, New York.
KGB Bar is a third place where you're almost always guaranteed a reading. One series, the venerable Drunken Careening Writers reading, has been going on every month for more than a decade. Finally, check out the nonprofit, all volunteer collective Bluestockings Bookstore and Cafe, for some queer/quirky and progressive events.