Well, here's a radical community-builder idea for your youth ministry: host a night in which you gather together...to do nothing!
Okay, maybe not "nothing," but pretty close. Rather than one more fellowship night organized around some crazy activity, high-energy games, road trip, or an hour or two of staring at a tv playing video games instead of interacting with each other, try this alternative. Announce to your group that your next meeting with be a "do nothing" night. You won't be organizing any activities. They are invited to come and bring their own activities, provided it's something they can do that will allow others to do their own thing without being disturbed. Youth might want to bring board or card games to play with friends, bring their journals and write, their sketchbooks and draw, read a book, or just hang out and talk. Perhaps have some quiet music ready to play, provide some snacks, and just let the group enjoy each other's company.
Believe me, most of our youth have schedules that are so overloaded that this one evening of sabbath time will be a real gift. And if you just can't resist the urge to "program," you conclude the evening with a short time of prayerful worship, focused on the spiritual practice of sabbath rest, perhaps using Exodus 20: 8-11 or Deuteronomy 5:12-15.