There are a few cruise lines which offer shore excursions for teens only. In Alaska, Carnival Cruise Lines and Holland America Line offer shore excursions geared towards teenagers. (Note that these teen-oriented shore excursions, however, are not available on Carnival and Holland America in their other cruising regions.) Disney Cruise Line has a lively teens only sunset cruise out of Nassau, Bahamas. Also, there is a teen designated beach on Disney's private island in the Bahamas (Castaway Cay) where you can play beach volleyball, snorkel, etc. with other youths your age. Lastly, if you and your parents are interested in cruising the Hawaiian Islands, then American Hawaii and United States Lines also feature shore excursions that are geared towards teens (biking down the side of a volcano and other active tours).
I hope this helps you find a cruise that you and your parents will love!
Luisa Frey Gaynor