The smoke from the New Jersey brush fire that's covering much of the city this morning is being held here by a low-level temperature inversion. In an inversion, the air is coldest near the ground and warms quickly with elevation. Hot air rises, so with cold air near the ground and not much wind there's no way to mix the smokey air near the ground with cleaner air above. As a result we're going to be stuck with widespread haze until late this afternoon, when rain ahead of an approaching warm front is expected to arrive.
The inversion layer is really shallow according to this morning's weather balloon launch. You have a good chance of breathing clean air at the top of the Empire State Building or other similarly tall building.
The warm front that will bring rain tonight is part of a strong system that caused flash flooding in Mississippi last night and is responsible for tornado watches being issued across the South this morning. New York is out of the tornado zone but we could see significant rain and thunderstorms overnight tonight. A cold front will put an end to the rain around tomorrow morning's rush hour and the rest of Tuesday is likely to be windy and warm with a high in the mid 60s. With highs around 60 degrees Wednesday and Thursday won't be quite as warm but there will be plenty of sunshine. The next chance of rain will be on Friday.