A while ago I was listening to the radio here and came across a radio drama. The language was perfect for my level as I could understand most of it as the dialogue was clear between the characters and the story was pretty simple to follow.

Unfortunately, I didn't make a note of the time or the radio station it was on. Does anyone know where I could find radio dramas to listen to?

You can search the iTunes podcast section and/or YouTube for オーディオドラマ and find quite a few, and also smaller number mark themselves ラジオドラマ.

(If you specifically want the ones on the radio, you can check here, http://www.nhk.or.jp/audio/ )

I hear you. I stumbled across a comedy recently called YOUR SMILE TOWN that falls into that bucket for me: http://www.tfm.co.jp/town/

Check it out on iTunes; you'll likely be able to find similar shows using that as a starting point.