Greenport Post Office 131 Front St, Greenport, NY11944 The Greenport Post Office is located on Front Street in Greenport adjacent to Mitchell Park. In addition to…More on-street parking, the Greenport Post Office has its own parking lot,which makes a quick trip to the post office possible. Post office boxes are available only during business hours. Passport application services are also offered in this post office location. Stamps and packaging materials are sold as well. Call for information on shipping prices or for more information on the passport application process.