Look for other threads about Key West. If your kids have not been exposed to raunchy, off-color or poor humor and you wish to keep it that way, do *not* go on Lower Duval St. Spend your precious time seeing the good stuff in Key West. I'm a frequent visitor to the rock and never recommend Lower Duval St. unless you just want $5 TShirt shops, junk souvenirs and over-exposed, poor quality bars. Don't get me wrong. Duval St. has its place for those who long for Mardi Gras all the time and prefer to drink overpriced drinks in the same places that everybody else drinks them. There's just so much more to that 8 square mile island than Lower Duval.
Hemingway House, Conch Train (or one of the trolley services), the Bight, Shipwreck Museum, Key West Lighthouse, Audubon House, Truman Annex (and the Truman Little White House), Key West Cemetery, East Martello Tower, Butterfly Conservatory, Mallory Square, Fort Zachary Taylor, San Carlos Institute. These are all better things to see than a shopping and debauchery district.
Food: Pepe's, B.O.'s Fish Wagon, Blue Heaven, Garbo's Grill, 5 Brothers, Bien, Eaton Street Seafood, Santiago's Bodega, Kojin, The Cafe, Sarabeth's, Rum Barrel, Turtle Kraal's, Dante's (where you can even go for a swim in their massive freeform pool), El Siboney, Louie's Backyard (and Afterdeck if you eat at the bar). These are but a few of the much better places you can eat than Margaritaville, Sloppy Joe's or Hogs Breath. You only have a short time there. Take the opportunity to go where the herd doesn't.