How was life different for slaves on big plantations, small farms, and the cities ?
Slavery was indeed a part of life in the city as well as the countryside. Statistically 95% of slaves in America lived on plantations or farms. This was true in part because of practicality and necessity. Farms required a large number of slaves to work the fields and do the physical work that needed to be done whereas the running of a house in the city required relatively few slaves by comparison.
Though it is not possible to speak of slavery of any kind as "good", it is probably the case that the more urban the setting in which a slave found himself or herself the better.
One of the reasons was living conditions. In the country the slaves were housed in shacks and barns close to the fields where they did their work. No insulation or comfort measures were taken in the construction of these facilities thereby making weather changes challenging. And clothing was sparse. Most slaves that worked the fields were given one set of clothes that were expected to last the entire year. Children were often given no clothes at all.
In the city things were different. Households that could afford slaves were usually large enough that the slaves could live in the attic, basement or spare rooms. By proximity they would benefit from the heating and insulation of the house that their country counterparts didn't have. In addition to that they were clothed better since they were seen more often by visitors to the home.
Punishments were more severe in the country since a beaten and bleeding slave could be kept out of sight more so than in the city.
The motivation for the differences in treatment was not so much a better view of the slaves as people in the city, but the reputation of the owners since things were more "out in the open" in the city.