Health data below the county level is unfortunately only available for certain statistics (AIDS and breast cancer). However, the New York State Department of Health provides "county health profiles" which include the most useful health statistics for each of the five boroughs.

NYSDOH County Health Profiles:

the bronx
brooklyn
manhattan
queens
staten island

breast cancer in new york city by zip code

AIDS in new york city, by neighborhood (pdf)
you will need Adobe Acrobat Reader to view this file. to get Acrobat, click here

united hospital fund nursing homes index (searchable)

Environmental data is available at the state, city, and borough/county levels through the EPA's website.

epa homepage offers an overview of all the data/maps available on the epa website

maps on demand offers users the ability to do queries on the types of enviromental information they want on specific areas, as well as links to other tools on their website

enviromapper allows users to view an interactive map of their area with listings and specifics on toxic release sites and hazardous waste sites as well as other features

treebranch.com has recently developed their new Hub, which includes information about national organizations and agencies that are working in areas of interest to NYC residents and citywide and local organizations.