I guess there's not much information out there on Yozakura Quartet, so I'll give random info here.
Hime, Kotoha, Ao, and Akina are all part of the Hiizumi Everyday Life Consultation Office. They solve problems in the town the police can't handle. Hime has super-human powers, Kotoha has the ability to materialize her words (for example, if she says "microphone," a microphone will pop out of nowhere), and Ao can read people's minds. What can Akina do? Since it'll be a spoiler I'll keep that a secret for now.
Currently there is a fugitive trigger-happy psycho on the loose, and the Hiizumi crew take on the case. This psycho was able to escape prison by jumping over a 10-meter high wall, which is why the Hiizumi decide to handle the case.
Can Hime, Kotoha, Ao, and Akina catch the psycho? What's the secret of the Seven Pillars that stand in the town? Who's the mysterious cat-eared man with glasses? Is the hat Ao wears the same brand as the one Coo (from Di Gi Charat) wears?
...Please read the manga to find out! (Disclaimer: Reading volume 1 will not answer some of these questions).
By the way, this is my Xth manga with a character named Hime.