Joyce Summers- Mother. Not at PLC, but frequently mentioned and lives in Sunnydale. Buffy visits home each weekend to check on her mother, her friends, and generally make sure the world isn't in immediate danger of ending.
Hank Summers- Father. Not in Buffy's life except on the few days they manage to get together to hang out and have father-daughter bonding time.
Claire Bennet- Buffy and Claire are the super-powered blonde cheerleaders who lack popularity. Claire got off on the wrong foot with them and Buffy ended up helping Claire after some harassment, now they're both in the same boat. Buffy would've gladly become friends with Claire even if they weren't stuck in similar circumstances. Buffy repsects Claire's willpower and guts in their situation... plus thinks she's pretty cool besides that. Probably her best friend at PLC.
Peter Petrelli- They like to save the world together. Against vampires, demons, the forces of darkness, general bad guys, and coffee stains. Peter is her iPhone of powers for all those things general Slayer abilities just don't cover. Plus, he gives her notes to get out of practice. Or class. You know, whenever it's important. Or not.
Albel Nox- Her first time at PLC, she got along pretty well with Albel. They weren't the best of friends, but they still got along pretty well. Second time around? Getting a little better, despite a rough reunion of her accidentally nearly breaking his ribs with a kick. Hey, it's his fault for sneaking up on her after she just finished off some vampires. He didn't get mad at her though and they talked. She's not sure if he thinks of her as a friend, but she figures anyone who can survive a kick like that and still talk to her willingly (and without insults) has to be close to being one.
Usagi Tsukino- In response to helping Claire, the cheerleaders of PLC started going after Buffy too. Usagi was the one who stepped up for Buffy regardless of whether she needed it or not. Buffy still doesn't know Usagi too well, but they've hung out a couple of times and she's definitely not disliking it.
Willow Rosenberg, Xander Harris, and Oz- Buffy's friends back home in Sunnydale. They're only mentioned in PLC but Buffy talks about them to other people and visits them on weekends.
Nathan Petrelli- He came to make sure she wasn't going to burn down any school buildings anymore, she talked him into dressing up as a punk rocker for Halloween. Buffy's pretty sure she likes him.
Soma Asman Cadart- They talked mostly because he was good at acrobatics and trying to help the cheerleaders, just kind of not great at how he was behaving during it. Buffy talked to him and tried to get him to understand that being a jerk wasn't the best option. He seemed to be apologetic for it, so she's not exactly on bad terms with him. They don't really know each other well enough to be on any terms though.
Kazuhira Miller- Probably her favorite teacher. Normally she hangs back in P.E. class and tries not to show off, but she doesn't hold back quite as much in his class as she normally would. Plus, she likes him enough to actually show up when she doesn't have something really important to do. They've both dealt with some crazy stuff and Buffy kind of enjoys listening to what he has to say. It helps that he knows about her "delinquent" record and doesn't really criticize her for it. The only thing they've really got to worry about is her tendency to burn down school gyms. Really, it's not like she does it on purpose.
Rupert Giles- Librarian, watcher, father figure. Not actually family but close enough, Giles is a huge influence in her life and Buffy looks to him for guidance and aid-- even if she doesn't actively listen to it all the time. Without Giles, she'd probably be dead by now though so she's pretty grateful to him. Even if he's NPC'd in PLC.
Kadaj Espere- It's complicated. They're friends first and foremost, but Kadaj wants to be in a relationship with her. She used to like him like that and wants to try that again because there's no reason not to... other than that she killed her last boyfriend to prevent the world from being sucked into a hell dimension and hasn't had much of a chance to get over that yet. Buffy's still going to try though, and who knows-- if Kadaj can keep his occasionally insane and violent comments to himself, they might actually manage it.
Ciel Phantomhive- They're not friends, but they don't hate each other. Buffy's got Ciel's permission (not that she needed it) to handle supernatural threats despite his claim that he will handle most of the situations outside of her jursidiction (as per his orders from the Queen, but Buffy doesn't know that). They're roommates right now, and even if they don't exactly get along, Buffy doesn't mind helping him out even if it means something as simple as sharing information or forking out aspirin to get rid of serious headaches.