In September 1796 Abraham Bradley Jr., an American lawyer, judge, cartographer, and assistant postmaster general, published the first postal road map of the United States, mapping post office locations, routes, and distances between them. He formally called this map, which was published in four sheets intended to be pasted together Map of the United States Exhibiting the Post-Roads, the situations, connections & distances of the Post-Offices, Stage Roads, Counties, Ports of Entry and Delivery for Foreign Vessels, and the Principal Rivers. Strangely he had a different title for the map engraved in the upper left corner of the upper right sheet of the map which read, A Map of the United States Exhibiting Post Roads & Distances by Abraham Bradley Jun. The first Sheet comprehensing the Nine Northern States, with parts of Virginia and the Territory North of Ohio. The map included a remarkable and innovative table that indicated times and days of the week to expect mail at various important postal coach stops along the primary eastern route. A reader of Bradley's chart could determine that a letter posted in the northernmost station at Brewer, Maine, could be expected to reach the most southern station St. Marys, Georgia, in six weeks plus four days, or 46 days of travel. Copies of this map were intended to be displayed in all large post offices in the United States.
Bradley served assistant postmaster general for 30 years during the earliest history of the United States Post Office Department, and was responsible for moving the federal government's post office from Philadelphia to the new capital at Washington, D.C., hosting the national post office in his own home for a period. Bradley's long employment during the tenure of five different United States postmasters general provided consistency to the post office and helped establish the budding postal service as a reliable provider. The detailed and innovative postal route maps that Bradley drew on his series of innovative maps contributed significantly to the efficiency of postal delivery.
In 1804 Bradley updated his map with a version that reflected the rapid growth westwartd of the new country. This was called Map of the United States : exhibiting the post-roads, the situations, connexions & distances of the post-offices, stage roads, counties & principal rivers. Presumably there were several printings of this as the copy reproduced in the Wikipedia is called the "earliest state of the 5th edition. Bradley published his last postal route map in 1825.
Regarding the history of Bradley's map and its variant states see Barry Lawrence Ruderman's raremaps.com at this link.