The first is Arcadian Books, located at 714 Orleans Avenue (just across from the Bourbon Orleans hotel). I found this place while trying desperately to escape from Bourbon Street. Orleans Avenue is a quiet little strip that joins Bourbon and Royal Streets.
The free books are left on the front stoop. Don't forget to go in though, because you are in for a cluttery treat of literary proportions!! Books everywhere.
The second place carries less literature, but is no less literary for it. It's a gorgeous little coffee shop called Royal Blend, located in the alleyway just before The Court of Two Sisters. Sit in the shade of banana trees and sip your frozen coffee confection, all while taking in pearls of wisdom from your free book(s). The books at Royal Blend are actually, on average, fairly light fare. But escapist reading is definitely not a bad thing, and you might need a little Anne Rice after reading the Oxford Anthology of English Poetry you picked up at Arcadia Books.