This is an application version of the NYC DOT's detailed 2018 bicycle map. Totally ad-free and no data connection is needed to browse it! It only needs permission to access your location so that it can mark you on the map, even in Staten Island :)!
The application itself is designed to be simple, with only one button to swap between the front and back pages of the map. Make sure your location services are switched on in your phone's settings (cell tower + wifi based location is usually enough in Manhattan).