I am not sure he used a specific map. He had traveled through North Georgia prior to the war in the 1840's in search of horses. The story is inAtlanta and Environs: A Chronicle of Its People and Events, 1820s-1870s.

On January 21, 1844, a tall red headed lieutenant, First Lieutenant in the U.S. Army then at Charleston South, Carolina received orders to report to Marietta, Georgia. He traveled by rail via Augusta to Madison where he took the mail coach. Passing through Marthasville (Atlanta 1847), he arrived in Marietta on February 17th. The journey took three days, for he had been delayed in leaving Charleston on February 14th.

Upon arrival the young Lieutenant reported to Colonel Churchill, Inspector General of the Army. He spent the next six weeks assisting in taking of depositions of Georgia and Alabama concerning certain losses by volunteers in Florida of horses and equipment by reason of failure of the United States to provide sufficient forage, and for which Congress had made an appropriation.

During his spare time, The Lieutenant repeatedly rode horseback to Kennesaw Mountain, from the summit of which he viewed the surrounding country including Allatoona Pass,eighteen miles to the north, He also found time to ride also by horseback to the Etowah River(Rubicon of Georgia), to Allatoona, and to the Indian mounds(Etowah) on the Tumlin plantation in Cass, now Bartow County.

Upon completion of their work in Marietta the party was ordered to transfer its operations to Bellefonte, Alabama. En route, again by horseback, the young Lieutenant familiarized himself with the country west of Marietta and around Rome. Two months later, the work of taking depositions finished. The lieutenant returned to Augusta upon his horse passing through Rome, Allatoona, Marietta, Marthasville, and Madison thence to Charleston and Fort Moultrie by Rail.

This assignment during the early months of 1844, gave the young soldier, the chance to study at close range, the slopes, curves and stretches of the terrain, a habit engendered by a single fondness for the earth. The information, carefully preserved in his memory, was to stand him in good steed. He returned twenty years later, not alone, and no longer a lieutenant. His name was William T. Sherman.

Footnote from Memoirs of General William Tecumseh Sherman, Written by Himself. (2 volumes. New York 1891) I 30-32
Llyod Lewis, Sherman, Fighting Prophet . (New York 1932)