Back to the list of districts
Since this is not a specialty district, building it won't affect your specialty districts limit for this city. What's more, multiple Neighborhoods may be built in the same city.
The Neighborhood epitomizes the Modern Era's tendency of people to abandon the rural lifestyle and move into cities. It provides the means to increase the Population of big cities even more in the late game, when you have already exhausted all other possibilities for Housing.
A common strategy is to replace Farms with Neighborhoods. Farms may not be that needed in the late game, as you gain other means of feeding your Population, and as the territory around your cities increases and gives access to more Resources. Note, however, that a tile with a Neighborhood doesn't produce anything but Housing, since it can't be worked at all.
Mr. Rogers lived in an idealized one, as do Big Bird and Cookie Monster. In truth, neighborhoods are rarely such functional social networks with friendly values, aspirations, and culture. With the advent of the Industrial Revolution, for the first time more people lived in cities than the countryside; given that transport was limited and slow, overcrowded and unsanitary tenements grew in places like London, New York, and Berlin so the factory workers and office clerks could be near their place of employment. Then came the telephone and automobile; suddenly those middle-class wage slaves could escape the teeming slums and ghettos and move to the suburbs. By the 1880s, London was surrounded by planned "estates" such as Wembley Park and Kingsbury Garden Village ... and soon so were most other industrial cities.