OVERLAND PARK, Kan.—More than half of America lives in the suburbs. The others, too, will be able to savor suburbia by coming to this Kansas City, Mo., suburb if local planners have their way.

Museum officials in Johnson County, Kan., propose spending $34 million to create the National Museum of Suburbia, a faux suburb where visitors could wander through a model ranch-style home, wonder at an exhibit of lawn furniture and topple pins on a re-created bowling lane.

Among...