If your ancestor died during a time when there might have been an obituary or a death notice, search every paper that might have published something. In an urban area, consider the daily newspapers and suburban newspapers that might have included a notice as well--especially if the ancestor actually lived in a suburb. For rural areas, consider all nearby newspapers, ones in the county seat, and perhaps ones in the nearest "large" town, which could be 40 or 50 miles away--especially after auto travel became popular. Newspapers in towns where your ancestor used to live might also have published a notice as well.
And always consider ethnic or denominational newspapers, even if they were not published near your ancestor lived.