If you’re about to pick up your rental car but don’t know much about Cutchogue, don’t sweat it. Here are some basic facts to help you get started.This town sits 19 miles to the northeast of East Moriches, and 280 miles northeast of Washington, the nation’s capital.It never hurts to know how many people reside in the place that you plan to visit. In this part of Suffolk County, the population is close to 3,300.