It isn't where I'd take my 10 year old (Key West is more geared towards "adult" themed entertainment), . . .
I'll always fondly remember my first trip to Key West with my dad when I was a teen. We visited the Hemingway house. At the Mel Fisher museum I ran into the man himself, though I had no idea who he was until then. We went out on a snorkeling boat, as I wasn't yet a diver. We went on a fishing charter and caught quite the haul of large mahi mahi (er, "dolphin" in Florida-speak), one of which my dad had a place cook for us that evening. We were at Mallory Square for the ritual sunset observance and street performers. Sure, the bars and Duval St. scene can overshadow that if you let it, but I think there's plenty for a youngster and parent to enjoy together.