Osage Beach is a good choice in that area, it's centrally located. There's a factory outlet mall with over 50 stores right on the main drag (Highway 54). Entertainment for the kids would include miniature golf, water parks, go carts, and something called Miner Mike's Adventure Town.

You should probably rent a car, though, because you may want to go up to Lake Ozark or Bridal Cave in Camdenton. Even in Osage Beach, everything isn't within walking distance, and you'd end up spending as much on cabs as on an economy rental, unless you're staying at a resort with shuttle service. You can pick up brochures for area attractions just about everywhere.