My younger sibling LOVES the Danganranpa series, and immediately bought each of them as they finally came to the states. I've never dug into them though. I might finally have to now. Anything Ace Attorney-ish is at least worth a try for me.
When you say rhythm game though, do you mean like you need sound to play it? I just usually play handheld games at school with the sound off, so that'd just be a bit of a bother for me.