Teens love to take control over their own activities, so having them start a special interest group and rotate leadership can fulfill that need and teach them something new at the same time. Book clubs are a common example, and libraries sometimes have meeting spaces where book clubs can meet for free. Other special interest clubs might include a cooking club with monthly theme meals or a gaming club where teens meet and play board, fantasy or card games. With investment clubs, students can learn about the principles of investing by buying and selling stocks with fake money and printing out a summary of each week's gains and losses.
Field trips are always a welcome activity for energetic teens. Even the smallest museums often offer free guided tours or student programs. Hands-on choices, such as science museums, are even better for restless teens. Outdoor activities can include group hikes, field-day type games at a local park with or without prizes, geocaching, ice skating, mountain biking or badminton. Some state and national parks offer ranger programs to teach students about local flora and fauna. Other trips can include excursions to historical sites, plays or musical performances, factory tours, local government or a nearby farm.
Have your group plan a special event. It can be anything from a theme party or dance to a charitable event to raise money for a local non-profit organization or a murder mystery dinner and party. A youth group could also organize a talent show or put on a play. Charitable organizations are especially in need of volunteers and would welcome a group of enthusiastic and energetic teens to come up with a creative way to solicit donations or volunteer hours.
Classes taught by volunteer "experts" can be a wonderful way for teens to learn about a variety of subjects -- anything from simple science experiments to firefighting to architecture. If one of your teens has a special interest, ask him to teach a class on the subject to the rest of the group. Alternatively, most parks and recreation departments offer low-cost classes year-round.