**Check Your Local Library**
This is an obvious one, but if you haven't checked out your library's website in a while, then it's worth a visit. Public libraries have become more and more internet savvy, and are making increasing amounts of resources available online. These often include the very types of newspaper archives and other subscription databases we're talking about here. I'm not talking about online-while-you're-sitting-in-the-library type access, either. These are online newspaper archives that you can access from home (or anywhere else), 24/7.
If you don't know your library's website address, it's probably on your library card. But if not, a quick Google search on your city name (or neighborhood name) along with 'public library' should bring up a link very quickly.