urg I thought I'd replied to this a few days ago, debs, but obviously I missed some crucial task, like pressing the "submit" button
We've just come back from Cala'n'Bosch, which is a great resort with 2 beaches and a marina to stroll round, even some rugged coastline to the east, (no shade though) and a 30 min walk along the coast to watch sunset near the lighthouse to the west. Also boat trips available, and a 20-30 minute bus ride to the old town of Cuitadella.
Our kids have grown up now, so we didn't stay at these hotels, but it might be worth you researching these...
Holiday Village Menorca - AI and 1 room apts, lots of activities but I don't know if there's a specific teenagers club
Sol Falco - also AI and 1 bed apts - more international (which you might or might not like) does have a teenagers club
Anyway, I hope this gives you some ideas, and I hope somebody with teenagers will post with advice
Now to press the "submit" button.....