Dick - Gymnastics is the most obvious one. When he was younger, Bruce initially didn't want him to compete in competitions, or even join a team, because Dick would have an "unfair advantage". However, he eventually gave in and allowed him to join the school's team. Another hobby he has is baking. In most cases, he is forbid from the kitchen, however he is a fantastic baker. He is also very good at making fantastic stews, which Alfred has even claimed to be better than his own.
Jason - He's a literature nerd, with a particular love for the classics; Jane Austen and Charlotte Bronte are his favorite authors. However, we all know Jason is a theater kid at heart. He did every school play at Gotham Academy, and though he hasn't acted in anything since his resurrection, he still goes to local theaters with Alfred fairly often. He's also a fantastic cook, and the only person in Wayne Manor (other than Alfred) to never receive any sort of kitchen ban.
Tim - Photography is Tim's favorite hobby. His first camera was one of the most meaningful presents from his parents when he was younger, winning several photography competitions. He hasn't indulged as often since becoming a vigilante. Barbara still keeps him on-call as her blackmail collector though, which he does happily. He's also into skateboarding, finding skate parks to be a nice escape when he needs time alone. Many of his photo shoots occurred at the skate parks, for very emotionally charged urban photography. Other than those, he likes disassembling things to see how they work. This destructive hobby was punished and frowned upon when he was younger, but when Bruce discovered that Tim enjoyed taking things apart, would start leaving things around for him to play with, like old microwaves, or failed bat-projects. Tim also loves comic books, of which he has an impressive collection.
Damian - Art is something Ra's looked down upon, calling it "weak" and "insubstantial in society". However, it was still something Damian enjoyed, so he had to keep his hobby a secret. He was terrified Bruce would kick him out, when he found the sketchbooks hidden in Damian's room, however Bruce just asked if there were any supplies Damian wanted. He's still a bit self conscious of his art, but he is more open, giving paintings to his family as gifts, and even entering in an art show. He still has a fascination with knives from his time with the League of Assassins, and enjoys collecting ones that interest him, particularly vintage knives, and unique knives made out of unconventional materials, or those with intricate designs. Jon was the one to get him into video games, which he denies enjoying, but the hours he's put into Cheese Viking would say otherwise.
Cass - Ballet was one of the first things she fell in love with after being adopted. It was so similar to how she was raised-people talking with their bodies-but without the violence she so loathed. She easily convinced Bruce to sign her up for classes, and for once, it was something she could do, to communicate with people in a way she knew well. Another interest she picked up was astrology. It was something fun that she didn't necessarily believe in, but was a comfortable guidance. Damian hand painted her a custom tarot deck, and she has a small collection of crystals she finds pretty. Zatanna has offered to enchant some of them for her, but Cass declined the offer, saying that giving them actual magic enchantments removes the aspect of belief that she found comforting. She understood that the black tourmaline necklace Bruce bought her wouldn't actually keep her safe, but it gave her comfort, and a sense of safety, especially because it was a gift from her dad. (author's note: I don't actually know that much about astrology, tarot, and crystals, so if anyone wants to add to this and give a more realistic description of how it works, I would love to see it)
Steph - similar to Dick, she is a gymnast, though not quite at Dick's level. She is also into martial arts and has taken a few classes in Taekwondo and Boxing, and whatever other free classes were being offered at the community center. Cartoons and anime are pretty big interests, as well as video games. She often jumps around from hobby to hobby, and has several miscellaneous skills in a little bit of everything. (author's note: a lot of Steph I based off of myself. She's a character I relate a lot to, so a lot of myself is projected into her. Her height and weight being one of them. However, that was also because DC doesn't seem to know what a human woman looks like, because most of the female characters in the Batfamily are 5'4" or 5'5", and around 120 lbs, including Steph. So I just borrowed by height and weight from highschool, when I was at peak physical fitness, at the gym 4 times a week, and doing 2 sports, once meeting 2 times a week and the other meeting 3 times a week. That would place her at 5'8" and 155lbs, which is far more reasonable for an active vigilante. rant over). She also feels like the kind of person who would be into scrapbooking. Most of her pictures are stolen from Tim, and the pages are brightly colored with fun stickers and glitter.
Duke - he gives off the vibe of a soccer player. However, because of his focus on school and crime fighting, he just plays for the rec team. It's a fun activity that he can enjoy when he was time, and also use to explain away his fitness level and injuries. He's also a huge movie buff, enjoying to analyze every aspect of the film, from the characters, to the camera work, to the framing of each scene. He isn't as interested in making his own movies, but gets very into it when he does. Quentin Tarantino is his favorite filmaker, however Damian has stared getting him into foreign films as well.