The Federal Reserve Bank of New York, which serves the Federal Reserve's Second District, is the best-known federal presence in New York City, and a reminder of the importance of the city to the national economy.
New York State's archives are the source for where state actions affect the city. It's photographs and other documents help round out histories of the five counties that make up New York City.
The National Park Services has a state-by-state list of sites the federal government has designated as landmarks. Scroll down to find the landmarks in New York. Use this list in conjunction with similar lists from the state and city.
You have to hunt through this website, as it divides New York's five boroughs into their respective counties, and then divides into different sites to search for (parks, historic buildings, etc.) The image is from Clay Pit Pond on Staten Island, which still offers horseback riding space.
The National Park Service embeds a list of New York City sites in a list of New York State sites. Some sites, such as the Women's Rights National Historic Park, has a New York City connection even though it is across the state in Seneca.
Columbia University's library offers a guide to city government and services for its students. This page can help with studies of the relationship between levels of government, and with the impact of the federal government on this urban area.
New York States administers some land in New York City, but more important for researchers is the role of state government in area environmental protection.