Through its Articles & Databases page, the New York Public Library provides access to numerous electronic resources that contain newspapers and other periodicals. Some are subscription databases available remotely with a library carrd, others are available on site at NYPL branch and/or research libraries, and others are open access resources available anywhere without a login. Searching on the word newspapers turns up more than 160 resources that can be filtered further by subject or availability. Access them here: NYPL Newspaper Resources.
See the Digitized Texts page in our Beyond Wikipedia research guide for links to additional newspapers, magazines, books and other texts online, including the archive of Life Magazine, the Making of America sites from Cornell and the University of Michigan, The New Yorker Magazine archive, the Modernist Journals Project, and more. Many of the resources listed are open access.