I totally love this thread. The answers have been insightful and hilarious as well. Here goes my few cents:
Cleon: He'd be with his lady Lincoln-- this week, as he obviously had a thing going on with a different chick (according to the orginal movie script). Aside from that, he'd be working out and keeping his head to the radio for infomation about stuff going on with other gangs, to see what else he could get the set into. He probably also read the local newspapers and magazines for insight about everything else. Lover of a really good Kung Fu flick or two.
Swan: I figured he'd be the one to kick back, suck down a brew and watch a game. Other than that, he would probably spar a lot with Cochise, Ajax and Snow. There would have to be some kind of 'friendly' rivalry between him and Ajax, though--it came through in the Furies fight... He'd also be carefully hiding a few solo missions, just to mix it up and get some excess bop outta his system.
Cochise: He'd be going to the strip clubs or other clubs with Vermin as much as humanly possible, and then pulling two, three, maybe even more strippers to the Warriors' hangout at the end of a long night of spending singles. Beyond that, sparring, going out starting the occasional brawl, and for some strange reason I see him dancing to that "Apache" song by the Sugar Hill Gang. Avid Bruce Lee movie fan and martial artist.
Rembrandt: My boy here would have to be a b-boy on the side. Also likely to carry around notebooks or sketchbooks full of elaborate tag designs. Probably even spray paints designs on tee shirts just for kicks. It seems to me that he would stick close to Snow, like a little brother of sorts. Since he and Fox were quoted as being best friends, they both could've been hanging out and scouting. Definite music afficianado, too-- helps the art come out easier sometimes.
Fox: As mentioned, out scouting with Rembrandt, or going solo. I believe he was wearing a cross necklace in the movie, so he may have been quietly into his own religious beliefs; also reading a lot and keeping in close contact with the gang's affiliates for a little 'word on the street'. He probably LOVED Star Wars more than anyone else in the clique.
Vermin: As mentioned, he'd hang tight with Cochise, pulling in as many chicks as possible. He probably wouldn't stray from intoxicating substances, either. Probably an avid collector of calendars and mags with pictures of the ladies. Not to mention-- food. Seems like he'd enjoy a nice afternoon of all you can eat buffet, but works it off... with the ladies or in a mean rumble. Maybe even a closet Disco Daddy and didn't want the others to know about it.
Ajax: Women, women, party, bop, booze, bop, women. And then more women on top of that. Sparring with aforementioned brothers, teasing Rembrandt to toughen him up a bit, women, bopping, calling in to that pirate radio station to see if he can get something going with the DeeJay, and 'bullying' Vermin to pony up some of those magazines... maybe an Arm Wrestling champion of the family. He probably does a little work with his hands, fixing things to even it out, and otherwise living in the weight room.
Cowboy: Kind of a toughie... I think he'd be an avid collector and builder of models, whether it's cars or airplanes. Maybe even a little whittling when he gets REALLY bored. Perhaps a lover of 50's cinema and those really good Western flicks. I could see him and Fox being good writers, too, kind of like, mental 'minutes takers' at the gang's meetings. Seems most likely to know a lot about animals.
Snow: He'd be the most likely to be sparring with his brothers, or playing DJ when the pirate station is off the air. Good dancer, and the one the others go to for hair product recommendations

. Making sure the others don't rip on Rembrandt TOO much. Other than that, a bit of quiet time and reflection (at the beach, of course)daily, highly likely to plan the occasional bopping strategy. Probably spent other available time out on the b-ball court or chilling out in a local park to simply people watch. Most likely to have a dark side that scares the mess out of EVERYBODY....