I would encourage you to visit all of these sites, as well as view the tutorials so you can get the most from these sites and find those interesting ancestor stories!
The grandaddy of them all has over 23 million pages of Old New York State Historical Newspapers. It is outstanding.
New York Heritage's New York State Newspapers site has a wonderful clickable map that identifies where all of the online newspaper sites are located. That map can be found at New York Heritage - Newspapers.
I have created tutorials for five of the New York online sites. Their links, and links to the actual search sites are listed below:
Hudson River Valley
Northern New York
So go get them articles. You will have lots of fun!