“Let’s Talk in Japanese”, which is badly named as it’s a monologue and not a conversation or conversation practice, is a good one. Tomo grades each episode by JLPT level. In his opening lines he says he made the resource because dramas and movies are too difficult and other stuff is boring. They’re around 10mins each and I really like them.
Nihongo Picnic is quite good too, and does have some conversation episodes.
For anime, try Studio Ghibli’s Ponyo. The characters are young and the plot is fairly simple, so most of the dialogue is too. I’ve been watching Ranma 1/2 on Netflix and that’s quite fast paced with slang dialogue, but still fairly easy to understand from context.
Practicing listening with JLPT mocks/past papers might be most effective though, as the listening sections have that distinctive style.