Where the shanties were.

Rule of thumb. If you want to find squatters in an American city the first place to look is along the waterfront.

1. In coastal cities you look to the tidal basins. In Brooklyn this would be Red Hook. In Los Angeles this would be Terminal Island.
2. Inland look to the river floodplains. Chicago's entertaining Streeterville sideshow notwithstanding, the real action was in the river bottoms. Goose Island for example was much more successful and longer lived. In Denver the whole Platte River bottom was a colony.
3. As a corollary look for improvements and reclamation projects. Dikes and levees in Kansas City, New Orleans, Memphis were excellent places to build a stilt house or tie up a houseboat. The dredge and infill projects of harbors also create a whole lot of land that no one owns or cares much about.

Next, look to the parks and public lands. This is for two reasons.

1. There was a lot of open land in convenient locations open for settlement. San Antonio, Texas, had a terrible time keeping people off of its school lots, and San Francisco's police were so tied up evicting people houses built in the middle of  streets, alleys, and private property that they had to tell the city that they no longer had the resources to also demolish houses built in public parks.
2. Many parks are built on land reclaimed from squatters. New York's Central Park is a well known example, but Kansas City and Minneapolis did this too.

 Neglected lands. This is the hardest to locate without specific references to guide your search, but the stories...

1. Estate battles are classic progenitors of shanties. As the different sides of the struggle slug it out in court there is no one with the authority to call in the police to evict the interlopers. The longer the fight goes on, the more established the new residents become. 
2. Speculative properties. Nothing spells neglect like absentee owner. Whole Midwestern cities sprang up on land owned by someone in New York or Boston. East St. Louis is my favorite example.
3. It is my perception that empty houses were less common in the past, so that may be why they figure less often in the nineteenth century than they do in the twentieth or the present.  If nothing else the real estate mess has given a whole new dimension to squatting. It is now possible to squat in the house that you bought while you await foreclosure proceedings to figure out who really owns the property. Which is really just a twist on the estate battle angle I guess.