Where is the best place to find public records, such as birth records for a specific state and date?

I am looking to verify the birth place of someone using free public records, specifically in New York. I have date and name information, but thats it.Where is the best place to find public records, such as birth records for a specific state and date?
Most states would call it the Department of Health and Vital Records, or some such thing. Try www.health.state.ny.us/vital_records/ or www.citidex.com/1839.htm. If it is for genealogy, try www.nysl.nysed.gov/genealogy/vitrec.htm.

Hope this helps.