Isle Esme is the tropical island that Carlisle gave to Esme, presumably because if he didn't get rid of some of his vast cache of money somehow he would have to start eating it. It also may be a little distraction for her from her questioning of him:

ESME: Carlisle, sweetie, what is it you and Aro keep doing in the bathroom all alone?

CARLISLE: Er... Uh... Hey, I bought you an island!

ESME: I'm totally distracted now, since I'm a dumb woman! :D

CARLISLE: Now I don't have to come out of the closet! :D

It is the place where Edward and Bella spend their honeymoon, and have their headboard-splintering OMG FABBULUZ SEXKS, as well as where the demon spawn is concieved. Apparently it has a native housecleaner who recognizes Edward from her cool native legends, because native legends are usually really, really convenient like that in Meyerland. Said housecleaner allows Edward to demonstrate his rather shoddy Portuguese Brazilian, and gives him a chance to completely confuse his own species with a different one, which is pretty damn impressive.

The island is described as being covered in jungle and white sparkly beach sand, identical to the Cullen's skin, because Meyer can't stop blathering about Edward's appearance even to describe something else that's patently idiotic.

Isle Esme is located many miles off the west coast of Brazil. This is strange, considering that the west coast is the only coast that Brazil does not have. Not only did Carlisle buy Esme an island, he built a coast for it to be on! He's so compassionate. (Or Meyer's an idiot who doesn't know which directions east and west are.) Go buy yourself an atlas, Meyer (and a brain). Here's what Dan has to say on Isle Esme:


Here's a little visual for you, Meyer

"They land in Brazil, hop on a boat for the rest of the trip, and arrive at a private island called "Isle Esme," which was a gift that Carlisle got for his wife, hence the name. I bet she has a closet filled with lavish presents from Dr. Cullen, such as Laptop Esme, Necklace Esme, Chunky Purple Bracelet Esme, Sears Gift Card Esme, and Nintendo DS Esme."

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