Most people would rather either be paid for doing their radio show, earn income from the ads sold during it, or at least do it for free and get the benefit of using it as a platform to promote their interests and parlay it into something even bigger.
If you are not interested in buying radio time on a local station, the next best thing is to convince the Program Director you've got some content that would benefit him. Take some time and listen to your local radio stations, especially on weekends. Weekends are the weak link for AM and FM because stations often pick up cheap syndicated or satellite programming to fill the void if they can't automate and voice-track. The is true of many talk stations.
Listen to what these stations are already doing and try to build a case for giving you a shot with your Podcast or Internet Radio show. What you want to do is find a good fit between a local radio station and the demographic it serves and what you do on your show.
Mail on CD or email your demo and written materials to the Program Director. Follow up with a phone call or email. Expect to be ignored. This is where it's going to get frustrating. Work on several stations at once and keep hammering it. See if you can get some feedback on your content and ask what you could to improve it and make it more apropos for the station. Understand that what you do could be improved and embrace any criticism. Incorporate the suggestions into a new demo and start again.