Mary, keep in mind that Lauterbrunnen is not a hub town. It is at the end of the line and located in an isolated valley. That means every train excursion from Lauterbrunnen and Interlaken is an in-and-out trip over the same route you've already travelled. I most certainly would not consider day trips to Geneva, Basel, or Appenzell--too much time on trains and switching trains to make it worthwhile. Lucerne, as Nadine suggested, might be worth it; but even that would make for a long day trip.
As others have said, there is lots to do in the Lauterbrunnen area, not just in the valley itself but going up to Jungfraujoch and the Schilthorn. You could also go over to Grindelwald in the valley to the east, up to Murren, Wengen and Schynigge Platte. These would give you lots of train rides. Also, you could easily backtrack into Interlaken and do a variety of activities. For example: boat cruises on either Lake Thun or Brienz, go to a castle (e.g., Thun or Oberhofen), go to the Swiss Open-Air Museum (at Ballenberg). Teens would enjoy all these activities.
Also remember that one mistake novice travelers often make is thinking they can go farther afield on day trips than is reasonable because they underestimate the travel time and energy involved. Just because timetables show something is possible does not mean the possible is worthwhile. I suggest enjoying and savoring all there is in the spectacular Lauterbrunnen area and forget about the long day-trips that will be too exhausting and rushed to be of any value other than chalking up "I've-been-there merit badges." I frankly think that once you see the Lauterbrunnen valley you will not want to stray far.