We took our 17 yo daughter to the Caribbean last year, and when she was 14 took her to Alaska. We've been on most all the Celebrity ships.
The Infinity has a teen-only Tower Lounge and Disco. Softdrinks, dancing, games and socializing are mainly there. Depending upon the weather conditions, there should be some music, games and bands by the pool deck. It's really hard saying though with the weather.
When we went (late July) it was cold, rainy and / or foggy every day. Our parents / sister and her partner went to Alaska on Celebrity last month, and they said the weather was gorgeous, sunny and high 70's!! Go figure...
Hope you have lots of fun though! 8)