We once rode to Coney Island from Brooklyn Heights and got a flat along the way. You can ask a stranger where the closest bike shop is, or you can use USA Bike Shop Finder, which quickly turns up the shop's precise location and phone number. But we give it a Bronx cheer for not including websites or the ability to add a shop it didn't know about. $1; iPhone only.
BEST ANDROID ALTERNATIVE: Bike Shop Locator (USA); free.