The Readex project -- now called America's Historical Newspapers, formerly Early American Newspapers -- has now released 9 series. I only have access to the first 5. All 9 are accessible through the NYPL. Series 7 claimes to hold the N-Y Evening Post from 1821 to 1876, and the Commercial Advertiser, from 1821 to 1876. It also includes the American, which if I recall, lasted into the mid or late 1830s. Readex has a way of boasting that it offers a 40 year file of a paper, but when I look, I may see that certain years are missing. When I look at a year that is covered, I may see that certain months are missing. When I look at a month that is covered, I may see that only 5 issues are there. So how much of the Post and the Commercial are really digitized at this point should be looked into.
The Gale project, called 19th Century American Newspapers, covers the NY Herald. As I recall, Gale claims to cover the Herald from 1803 to the 1840s, even though there was no newspaper called the Herald published throughout that span. There was a Herald in the early 1800s, maybe one or two other short-lived Heralds in the teens and twenties, and then from the mid 1830s until 1824, the Herald founded by J. G. Bennett. And Gale's coverage of Bennett's Herald is missing at least one full year from the 1830s -- I tried looking for something yesterday.
The Godfrey Memorial Library, a genealogical library in Middletown, Conn., offers home access to the Gale file for a membership fee of appr. $100. They throw in series 1 of the Readex files, too.
When I opened your message, I was hoping you were calling for recommendations of NYC papers that ought to be digitized. I was prepared to nominate the New-York National Advocate, 1824-1826 (which is not the "National Advocate" which Readex claims to have digitzed, but hasn't, except for random issues), and its successor, the New-York Enquirer, 1826-1829. As far as I know, the N-YNA hasn't even been microfilmed, and the NYPL has filmed only half of the Enquirer. Very good files of both are in your own New-York Society Library.
GAT