There is a problem in giving him the ability to wander off at night – his phobia is minor.? If he is an agoraphobe best make it full blown, otherwise it is a mere inconvenience as appose to a genuine obstacle.

In A Beautiful Mind – Russell Crowe’s character’s mental condition is so severe that he hallucinates over several years people and conspiracies which coincide with reality to the point that he can’t distinguish between them.

In Rain Man – Dustin Hofman’s character’s condition isolates him from reality to the point that he is incapable of caring for himself on his own.

In Matchstick Men – Nicholas Cage’s character’s condition causes him to fall into crippling fits that disable him altogether.

If you look back through the lineage of MCs with mental conditions, they are all ‘full-on’ problems. The conditions make it so the characters are always on the brink, and all it takes is one thing to be out of place for a disaster to happen. However, in the case of your character, he can walk out at night and work in a bar. For an agoraphobe, I’d say he’s doing just fine and mostly over the problem, especially in New York – a city that never sleeps.

Again, I’m not sure you can rationalise these conflicting issues as they present a few fundamental logic flaws. If you are genuinely interested in writing a story about a character with a severe mental condition, and specifically an agoraphobe, perhaps there is a more logical obstacle rich premise you could put him or her in?