National Museum of the American Indian does a great job with the story of NY Indians.

Here's a link for the story of the Indians who once lived in Manhatten.
Too bad the story of DC Indians isn't told as well in DC!

http://nmai.si.edu/sites/1/files/pdf/education/Manahatta_to_manhattan.pdf  (This link no longer works, see update below)

 
The Lenape lived in Manahatta, now called Manhattan, prior to European contact. The word Lenape (len-AH-pay) means “the people” in their langu age. The Lenape spoke an Algonquian language, one of many families of languages in North America.  ...

.May 2023 update

Some time after this post, the NMAI seems to have taken down the Manahatta to Manhattenan pdf praised above. Why that was done is unclear.

Readers can still review the pdf, which is posted on a Native American educational site based in Washington state:

Manahatta to Manhatten PDF from Washington state