Club Med Punta Cana
I've been there many times since I was 12, both as a teen and an adult, and they have a ton of things to do for everyone. There is a teen club, with their own hangout with pool and foosball among other things, but they also do all sorts of other coordinated activities with the GOs (basically their camp counselors) such as archery, beach volleyball, soccer, flying trapeze, pool games, etc.
The resort is absolutely beautiful and has a great beach, as well as a huge pool.
Like I said, I've been there quite a few times, so if you have any other questions (or want to see pictures!) let me know!