Ahoy Bilgemonkey. I have been to Key West once about 6 years ago. I remember seeing many teenagers, as well as families there. As Monsieur Hurricane mentioned the cemetary there is really awesome especially the monument to the USS Maine victims (Spanish-American War). If me memory serves correctly, there is one of those god-awful Ripley's Believe-it-or-not museums, which always appeals to "that age" group, as well as lots of cool gift shops, bars, restaurants, museums, a vintage aquarium, the fabulous sunsets, scuba diving and boating tours. And, don't forget to visit Jimmy Buffett's store! The drive through the keys on US 1 (Overseas Highway) is spectacular in itself.
Ye must also be pre-warned (if ye have never been to Key West), that it is one of the gay community's Crown Jewels, so be prepared to see some outrageous sights! Just be open-minded to these things, if ye and yer family visit the island.
It truly is a great vacation spot. I highly recommend it to anyone. :)
Captain Ciaran