A great hand-drawn map of Hooker’s Division from the Library of Congress:
The territory indicated from the accompanying diagram is in Washington, D.C. and is known as “Hooker’s Division.” During the Civil War it was occupied by the camp of General Joe Hooker’s troops in their defense of Washington. Since then it has become the plague spot of Washington, a center of vice, liquor-selling, and prostitution, such as is characteristic of all High-License cities. It is in the very heart of the city, extending along Pennsylvania avenue to the United States treasury. The four daily papers of the city, Post, Star, Times, and News, are published in this territory. Within its borders are the lending banks, opera-houses, and hotels.
This district alone contains 100 regular houses of prostitution, exclusive of assignation houses, 31 of which are in the single block surrounded by C, D, 13th and 13 ½ streets northwest. Besides this there are an even 50 saloons, most of them run directly in connection with bawdy-houses.
Each one of these 100 houses of prostitution sells liquors openly and freely every day, and not a single one pays the $400 local license. There are 61 bawdy-houses in this district which hold Federal permits, while the other 48 pay no license whatever.
Grover Cleveland can sit in his bedroom window at the White House and survey this entire territory. He is within sight and gunshot of each of these 169 dens which defy the laws which he is supposed to execute through his commissioners. The following is a list of 61 persons in this district and their addresses who are selling liquor under Federal permits and who do not pay the $400 High-License:…
the location 
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This map probably dates from February 1896 and was developed by the “Anti-Division Association for the Suppression of Vice in the District of Columbia,” an anti-prostitution organization. The supposed relationship between Gen. Hooker and the red-light district mentioned in the text was popularized about this time among those who had not been in Washington during the war and did not know the real reason for the name. Hooker’s troops were never quartered here nor did he have any particular connection with D.C. prostitutes, such as compelling them to reside in this area. “Hooker” was a slang term for thieves and prostitutes by the 1840s, and when the allegedly dissolute Hooker and his military Division became famous, fun-loving Washingtonians applied this famous name to DC’s premier red-light neighborhood.
This is great, Mark! Thanks for commenting!