Since Hudson seems to be quite popular in this subforum, I found a couple of interesting things on its Wikipedia page in the "History" section 
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Hudson is quite narrow, with just four streets forming the bulk of the grid: Union Street, Warren Street (formerly Main Street), Columbia Street (formerly Diamond Street), and State Street. When there was space before you fell off a cliff, other streets were added.
Originally Columbia Street was the connector in orange from the street grid to Columbia Turnpike which deflects off to the southeast. The portion in purple was Union Turnpike.
The turnpikes developed in the late 18th century when the state would charter a turnpike company. The company would create an improved road, and then charge a toll for its use. A turnpike is literally a pike mounted horizontally which could be turned (rotated) to permit a wagon or carriage to pass. There would be a tollhouse, adjacent to the turnpike with a barn or other outbuilding on the other side. This would make it difficult to go around and avoid the toll. There is tollhouse on Columbia Turnpike just outside Hudson.
The alternative to turnpikes would be public roads. Each town would have road districts, in which landowners were assessed a tax paid in labor. You might be assessed two days labor, an you or your slaves would spend two days cutting trees, removing logs, etc. Without any power equipment, you are more likely to create a road by finding a route that doesn't have obstacles.
The deflection from the street grid to the north was necessary to avoid Prospect Hill. Columbia Turnpike and Columbia Street are thus on a shoulder of Prospect Hill (known as Academy Hill). Green Street was developed further down the hill to avoid even that terrain.
Around 1910 two portions of Diamond Street were renamed. The area west of 3rd Street (in Green) was renamed Fulton Street. I suspect there is a connection to the Fulton centenary (Robert Fulton developed the first commercial steamship in 1807). This was also near the tricentennial of Henry Hudson's 1609 voyage up the North River in the Half Moon.
The portion east of 5th Street to Public Square (in blue) was renamed Gifford Place, after a prominent Hudsonian.
The Red Light district was between 3rd Street and 5th Street (in red). The only reason that it makes sense to rename parts of the street is if you wanted to disassociate yourself from the activities down the street. If someone inquired about "Diamond Street" it would be clear what they were seeking, and they would be less likely to accost someone on Fulton Street or Gifford Place.
Later all five segments were renamed to Columbia Street.
Gifford Place lives on in the city charter.
"to a point where the center line of Gifford Place intersects the center line of Columbia Street, and thence along the center line of Columbia Street and the center line of Columbia Turnpike"
Instead of Columbia Street intersecting Gifford Place, Columbia Street now makes a slight turn to the north. And the fact that Columbia Street now continues east of Columbia Turnpike may have caused the charter to be ignored and a portion of the 5th Ward being treated as if it were part of the 3rd Ward. One reason the previous mayor may have vetoed the measure ordering the Board of Elections to follow the charter is that he lives in that area, and was elected as 3rd Ward Supervisor when he didn't according to the charter live in the 3rd Ward.
Apparently the brothels were quite discrete. I haven't found any evidence in census records of a predominance of females in that area, so they did not exist for census purposes. If they went out to shop they would dress demurely. If the madams made payment to the right officials there was no reason to bother them.
