Your kids are probably just the right ages to appreciate the charms of this often-overlooked Disney classic.
Tom Sawyer's Island is actually two islands connected by a long suspension foot bridge. You get there via raft (the dock is located next to Big Thunder Mountain Railroad). On the Island, kids can run down the trails that cross the island, and explore environments taken from and inspired by "The Adventures of Tom Sawyer" and "The Adventures of Huckleberry Finn" by Mark Twain (it may be a good idea to screen
one of the many movies these books inspired before your visit so your kids will appreciate the Island). There's the "Mystery Mine" (where water flows uphill), Injun Joe's Cave, Harper's Mill, Aunt Polly's Landing (home of the only Coke vending machines in the MK), and Fort Langhorn -- a western-style fort where kids can fire rifles and slip through the Fort's escape tunnel. On top of the Island's tallest hill is Tom & Huck's Scavenger Fort, a playhouse where they'd pretend to be pirates (complete with the Jolly Roger flying above the fort). Near the scavenger fort is a picnic area that is one of the most secluded and tranquil spots in the Magic Kingdom -- and an excellent place to enjoy a lunch brought over with you from the Mainland. Very recommended as a place to slow down for an hour or two. For my final recommendation, just see the quote in my signature at the bottom of this post.