As of the census of 2000, there were 1,631 people, 590 households, and 493 families residing in the village. The population density was 320.3 people per square mile (123.7/km²). There were 617 housing units at an average density of 121.2/sq mi (46.8/km²). The racial makeup of the village was 85.71% White, 4.90% African American, 0.12% Native American, 7.54% Asian, 0.06% from other races, and 1.66% from two or more races. Hispanic or Latino of any race were 2.08% of the population.
There were 590 households out of which 33.4% had children under the age of 18 living with them, 77.8% were married couples living together, 3.7% had a female householder with no husband present, and 16.3% were non-families. 12.7% of all households were made up of individuals and 4.7% had someone living alone who was 65 years of age or older. The average household size was 2.76 and the average family size was 3.02.
In the village the population was spread out with 24.5% under the age of 18, 4.8% from 18 to 24, 18.8% from 25 to 44, 37.0% from 45 to 64, and 14.8% who were 65 years of age or older. The median age was 46 years. For every 100 females there were 100.9 males. For every 100 females age 18 and over, there were 99.2 males.
The median income for a household in the village was $161,292, and the median income for a family was $181,443, but the central regions of River Hills tend to be much wealthier than the outlying regions. Males had a median income of $100,000 versus $54,167 for females. The per capita income for the village was $94,479. About 0.4% of families and 1.7% of the population were below the poverty line, including 1.3% of those under age 18 and 1.3% of those age 65 or over.