The Obituary App:

A mobile application that houses obituaries and correlates them directly to corresponding cities and people. This is a completely free resource.

Websites: 

A Funeral Home’s website is a great place to publish an obituary, and in most cases, is free to do so.

Newspapers:

Small towns are still sometimes free to submit or have a nominal fee.  Larger cities or corporate publishers charge by the character and can be extremely costly.