Our last two trips have been to the Poly. We absolutely love it. My DS is 11 and DD is 9, so we aren't quite in the teen years yet, but here's a couple of ideas for you.
We tried DQ for the first time this March (we evacuate New Orleans for hurricanes and Mardi Gras!), and it was fun, but very NOISY! I didn't find it especially relaxing, but there were a few attractions that were really good. The bumper cars where you shoot volleyball size balls at other cars (the riders are protected by plexiglass) and make their car spin, the virtual pirate ship where you stand on a real deck shooting cannons, and the ride where you design your own rollercoaster were all fun. But if you're looking to unwind, this is not the place.
Poly tips: We rented the Surrey Bike and rode the paths to the GF and around the POLY one day. It was really quite nice. I think it's a great way to spend an hour. You can cover the whole area in that time. We looked into the little speedboats, but my kids aren't old enough to drive them, so we didn't do that. It looks like fun to me though! There are walkways along the beach and lake which the kids enjoyed exploring. Not much to explore but still a nice way to spend an evening. Look for our "secret path" as the kids called it. There's one path that ends on a point behind the Poly and has a great view of the lake, GF, Space MOuntain. The walkway ends with a cement circle. We just laid there looking at the stars for a while. One of those magical moments with the kids... We love Kona Cafe! The food is great and the deserts are fabulous! My DD always got the Kiddy Cone and DS got the Kiluaua Tort (very chocolate!). In fact I just booked a last minute trip for Jul 6-11 at the AKL with a great passholder rate and the only other resort we plan to visit is the Poly for dinner and desert one night.
Since we usually go in Feb or Mar, this is the first trip we plan on trying a water park. and mayyyyyyyyybe miniature golf. I'm trying to think of things to do to get away from the parks for a bit as well. Final suggestion: I didn't know anything about AKL until after I booked it. You may want to check it out one afternoon or evening. Boma is supposed to be an excellent buffet, and the 3 savannahs with animals roaming sound nice. There is storytelling around the fireplace in the great lobby balcony overlooking one savannah, and they even have night vision binocs for you to use!
Sorry this is so long. Hope it helps and have a great time!
Eric