Two new Gini-type spatial inequality indices are introduced to measure the average degree of income inequality within individual neighborhoods and the inequality of average incomes among individual neighborhoods. Connections with geostatistics and the asymptotic distributions of these indices are investigated. A rich database from the U.S. census is used to study spatial inequality in the 50 largest American metro areas during the last 35 years. Four different types of cities are identified along the lines of inequality between and within individual neighborhoods. This latter is shown to be associated with lifelong economic opportunities and life expectancy of urban residents.