As well as advertising jobs newspapers also supply up to date information about which companies are moving into the area and which are expanding. You can use this information to apply to those companies before they advertise.
To find out which local newspapers are published in your area, follow this link. Alternatively for an interactive map showing local newspapers use this link.
the majority of local newspapers have websites, many of which have job search engines or a list of local jobs, allowing you to search for local employment online.