Squall Leonhart- Quistis is fascinated by Squall and for a brief while before she gets her childhood memory back, she thinks that she has fallen in love with him. She grew up with Squall in an orphanage by the sea with the entire Orphanage Gang and she was like a keeper for all the children back there as she was the little bossy Quisty. As she grew up, Junctioning with a GF made her forget about her early childhood and when she met Squall once again, she felt memories coming back to her, but she wasn't sure what they meant. She took an interest in him and eventually thought that she was in love with Squall. Later, she realized that that feeling was that "protective" big sis instinct.
Rinoa Heartilly- Quistis doesn't really have any direct relationship with Rinoa as a good friend. When Rinoa entered the picture she totally gave up hope of ever getting Squall for herself. She hid in the backgrounds for a while and eventually realized that Squall and Rinoa should be together and she knocked some sense into Squall to go and rescue her (for about the five hundredth time might I add...). I'm assuming that they're not that close. Quistis is further away from Rinoa than she is any other character. Not much action between these two. At least Quistis was nice enough to let Rinoa have Squall... But poor Quistis...
Selphie Tilmett- She is one of Quistis' transfer students, so I'm sure that they're pretty good buddies. Selphie is always happy and interacting with Quistis, so they should have a pretty good relationship. As teacher and student, Quistis doesn't really act like "one of the gang" that much, but I'm sure that Selphie brightens her day all the time!
Zell Dincht- She's always trying to keep Zell under control as he is one of her more crazier students. She is really close to him as they were friends when they were kids in the Orphanage. While Zell acts hyper and childlike, they really are pretty close, even if Quisty can be a little boring sometimes, she still cares for Zell very much.
Irvine Kinneas- While Quistis finds Irvine's ladies' man attitude a little annoying at times, she is very close to him as he protects her most of the time. Though it's not really announced in the game, I'm sure that Irvine has a very close relationship with Quistis and he really respects her. They grew up together in the orphanage by the sea. Irvine even had a little crush on Quistis when he was decided which of the three girls to go for. "Selphie, Rinoa...or Quistis... Selphie...Rinoa...or... Quistis.." He sure has a tough time, doesn't he?
Seifer Almasy- She's always though of Seifer as a troubled young man ever since they were children in Edea's orphanage all those years ago. Once at the Garden, Squall and Seifer began to squabble again and Quistis' instincts to break up the fight made her take notice in Squall. She almost seems a little fearful of Seifer because of his unpredictable personality. At least in the end, Seifer becomes somewhat of a normal person again. I also hear a lot of people think that these two would make a cute couple. I think they do look cool standing next to each other, but... their personalities are too different. Quistis would probably go crazy after one date with this guy!
Laguna Loire- Quistis doesn't have much of a relation with him at all. She never knew him during her childhood and just recently met him when the gang went over to the capital of Esthar. Though he took care of Ellone, they really didn't meet. I'm sure she'd get stress over meeting an airhead like him. J/k
Ellone (Leonheart/Loire?)- Quistis really looked up to "big sis" when she was in the orphanage. After Ellone left the orphanage, Quistis took it upon herself to be the second "big sis" and to watch over everyone. She truly loved Ellone dearly and I know she still does though she seems more mature than Ellone is now, but still... They go a long way back. I think Quistis is closest to Ellone of all the characters in the game except maybe to Edea.
Edea Kramer- Edea, also known as Matron to the orphanage group, took care of all the children at the orphanage years ago. Quistis looked up to her greatly and really loved her like a mother. After the GF's effect took its toll on Quistis' mind, she didn't remember Matron. Matron on the other hand, had been possessed by a Sorceress from the far future and was wrecking havoc on the world. Quistis and the gang are sent out to destroy her. After Edea returns to her former state, all the orphanage group's memories return and they have a happy reunion with Matron.