Note: This is speculation based on what we know of the curse and the character histories within the show. The exact circumstances of Baelfire's escape from Neverland haven't really been shown (and may shed more light on his relationship to the curse - remember, it was made just for finding him), and we're currently on the midseason break immediately after the curse was broken - so a definitive answer is likely to come along once the season resumes in March.
That said: He may or may not have been sent back to the Enchanted Forest -
we don't actually know yet, but I expect he was sent somewhere else in our world.
Regina said that she could give Emma memories of not having given up Henry - so we know that Neal still left Emma in her memories. He left her because of Pinocchio's message, and Pinocchio, like Emma, was unaffected by the curse due to having come through at the same time as she did.
So all three of them could easily retain their true memories up until the point where Emma gave up Henry, without conflicting with the conditions of breaking the curse.
Part of breaking the curse is erasing everyone's memory of it - including Emma's, who was never affected in the first place. So this would include Pinocchio and Neal, who would now live in our world without remembering Storybrooke at all. And since Mr. Gold effectively didn't exist, Neal's memory of meeting Henry and Emma again was likely also erased.
All the above holding true, he would now still live in New York City and have no idea what happened to the woman he left all those years ago.
UPDATE: As of 3x12, parts of this answer have been invalidated, but the "why" part of the question still isn't completely clear:
Neil/Baelfire did get sent back to the Enchanted Forest. We don't yet know about Pinocchio/Austin. Neil's apartment in New York City was not only untouched, but Henry's camera was still there, too, after he left it behind the first time.
So at the moment, breaking the curse appears to have directly affected only things within the Storybrooke town limits, with the exception of Henry and Emma. Neil/Baelfire was within town limits, and so he was affected, but it's not clear why he couldn't have just left with Emma and Henry.