NYC Bus & Subway Maps This free app is essential because when you are down in the subway you will not get reception so having a subway map downloaded to your phone makes sense!
Food Truck New York This app lists many of the food trucks in New York and it updates - usually weekly. I used it successfully to find a green food truck.
New York Travel Guide – mTrip This app from mtrip is US$5.99. It's a trip planner for New York City with some very snazzy features including augmented reality, electronic postcards, travel guides, and itinerary tools. It's an offline tool.
New York News A great free way to keep in touch with the local NYC news from about a dozen sources.
tkts This free app is the best way to get all the listings of Broadway and Off-Broadway shows that are sold at the TKTS discount booths. A good tip for those looking to see a live show at a discount - you can use this app instead of going to see if there are tix available.