The New York City Housing and Neighborhood Information System (NYCHANIS) is an extensive, searchable resource for housing statistics in NYC. They get their information from a number of "official" sources, including the NYC Housing and Vacancy Survey, which is where the following data came from.

Finding information on the sub-borough level (i.e. by neighborhood) can be difficult. Is the agency gathering the data looking at census tracts, community boards, or ZIP codes? Each can lead to very different results. And while there may be community groups that have figures on average monthly housing costs in the specific neighborhoods in which they operate, obtaining those figures can mean a lot of footwork.

For this question, which needed a quick turnaround, I stuck with what I could find in NYCHANIS. Here's some of what I found:

Brownsville/Ocean Hill (Brooklyn)
Median Household Income in 2002: $27,000
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 28.6%
Median Monthly Contract Rent in 2002: $555
Median Monthly Gross Rent in 2002: $625
Median Percent of Household Income Spent on Contract Rent in 2002: 25.6%

Brooklyn Heights/Fort Greene (Brooklyn)
Median Household Income in 2002: $41,000
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 17.7%
Median Monthly Contract Rent in 2002: $736
Median Monthly Gross Rent in 2002: $805
Median Percent of Household Income Spent on Contract Rent in 2002: 24.0%

Mott Haven/Hunts Point (Bronx)
Median Household Income in 2002: $15,000
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 44.6%
Median Monthly Contract Rent in 2002: $448
Median Monthly Gross Rent in 2002: $495
Median Percent of Household Income Spent on Contract Rent in 2002: 27.6%

Riverdale/Kingsbridge (Bronx)
Median Household Income in 2002: $45,000
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 13.7%
Median Monthly Contract Rent in 2002: $716
Median Monthly Gross Rent in 2002: $800
Median Percent of Household Income Spent on Contract Rent in 2002: 22.2%

East Harlem (Manhattan)
Median Household Income in 2002: $18,000
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 33.5%
Median Monthly Contract Rent in 2002: $495
Median Monthly Gross Rent in 2002: $511
Median Percent of Household Income Spent on Contract Rent in 2002: 29.0%

Upper East Side (Manhattan)
Median Household Income in 2002: $79,700
Percent of Households Below the Federal Poverty Line (Poverty Rate) in 2002: 5.1%
Median Monthly Contract Rent in 2002: $1,300
Median Monthly Gross Rent in 2002: $1,396
Median Percent of Household Income Spent on Contract Rent in 2002: 24.3%