Answer:
Approximately 2 miles (3.22 kilometers). According to the measurements I got using Google Maps and a tape measure, Manhattan Island is exactly:
2.06 miles (3.32 km) or 10,888.88 feet (3,318.93 meters) wide at 33rd Street
2.06 miles (3.32 km) or 10,888.88 feet (3,318.93 meters) wide at 40th Street
2.02 miles (3.25 km) or 10,666.67 feet (3,251.20 meters) wide at 47th Street
2.02 miles (3.25 km) or 10,666.67 feet (3,251.20 meters) wide at 52nd Street
2.10 miles (3.38 km) or 11,111.11 feet (3,386.67 meters) wide at 58th Street