Missouri really has a lot to offer... plus it's easily within driving distance. We visit the Ozarks every year for the past 6 years (we have a 3-year-old daughter) and find it very relaxing and we never run out of things to do.
St. Louis -- The Jefferson National Expansion Memorial (a.k.a., the Arch) and Courthouse, Ulysses S. Grant National Historic Site, Grant's Farm, The Budweiser Brewery, Six Flags, The Magic House, a zoo, baseball, and Meramac Caverns.
http://www.explorestlouis.com/
http://www.magichouse.org/
www.nps.gov/jeff
www.nps.gov/ulsg
http://www.grantsfarm.com/
http://www.americascave.com/
Kansas City -- Great Wolf Lodge, The Country Club Plaza, Harry S Truman National Historic Site (Independence, MO), American Jazz Museum, National World War I Museum, Boulevard Brewery, The Negro Leagues Baseball Museum, Science City, Hallmark, Worlds of Fun, Oceans of Fun, Schlitterbahn, T-Rex Cafe, American Doll store/salon/restaurant, and of course BBQ.
http://www.visitkc.com/index.aspx
Branson -- shows, shows, shows; Lambert's Cafe (Ozark, MO), Wilson's Creek National Battlefield (Repbulic, MO), Silver Dollar City (fun for the kids & parents), lakes, a zipline, caving tours, ride the ducks, Table Rock Dam, the fish hatchery, Indian Point, Dewey Short Visitors Center, Table Rock Dam tours.
http://www.branson.com/
www.nps.gov/wicr
http://www.silverdollarcity.com/
http://www.throwedrolls.com/
http://www.bransonzipline.com/
http://www.missouricaves.com/
http://mdc.mo.gov/regions/southwest/shepherd-hills-fish-h...
http://www.swl.usace.army.mil/parks/tablerock/recreation.htm
http://www.tablerockdamtours.com/press-release-group-tour...
For more National Park Service information and the America the Beautiful Park Pass (good at Corps of Engineers, National Park Service, and US Forest Service locations) see www.nps.gov