The Persona games are a huge thing in Japan and is not for free, they are really great games if you enjoy the "dangeon crawler" type of games with some RPG elements on it. The game has an interesting list of characters and a involving story. Is the kind of games that even though it has a main story to follow, it has plenty of side quests and many things to explore besides that. It has a great replay value. Even if you are mostly a RPG fan, the game is not going to dissapoint you. For me is one of the "Must have" games for the Vita.
(Persona 4 Golden is a remake of Persona 4, an RPG/sim for PS2.) The gameplay consists of controlling your character during his free time (jobs, social interaction, school work, etc.) and exploring dungeons inside of a TV station. Your character encounters shadows there which can be fought with Personas, alternative forms of shadows that are manifestations of aspects of one's self. The bonds that your character forms with people you meet correspond to the strength of various Personas (via Arcana). Combat is turn-based. You'll fight bosses as well. The dungeons are beautiful and the story involving. It's worth buying for any open-minded gamer.
I spent ~50 hours playing Persona 3 without losing interest over ~2 months. I have read that a playthrough of Persona 4 could last 100 hours. Persona 4 Golden has slightly more content, adding replayability. There are multiple endings.