Places someone might find the character? Things they might be doing? Everywhere he can find people. Mostly he'd be any where that could constitute as a commoner place doing things he considers commoner activities. Which is mostly any recreational activity in the prison except parties, school, and breathing. He'd also be in a music room occasionally since he likes playing piano.
Is the character in any IC group, including the school? Details! Tamaki would be taking classes at the school but I can't remember which ones. And the Host Club, which he founded.
What kind of person does the character get along with? Tamaki gets along with everyone as long as hey aren't a bad person. He tries to see the good in everyone and until you do something completely unforgivable he'll always treat you as a friend. Even when he's terrified of you because you practice some evil form of magic, which is most magic because he has no experience with it other than some basic magician tricks and the Black Magic Club.
Is there any type of CR you feel the character is missing (e.g. romantic interests, mentor figures, etc)? Tamaki needs some sort of CR with everyone. And he has not tagged everyone. That should change.