When trying to think of a serious game it seemed natural to learn towards a sim-style of play. SimCity to SimEarth to The Sims all reproduce aspects of society in an easy to understand and easy to control way. My idea for a serious game would be a simulation of community arts.
The player could begin the game with a small theater, art gallery, or music hall. They would need to properly manage this business in order to expand the size of the space, as well as add community outreach programs like classes, summer camps, and scholarship programs. The player could make money with shows, grant applications and fundraisers. Different things would work best depending on how the community views the player. The more the player has done to revitalize the community, the more support they will receive.
I would want this to be a highly visual game. The space the player controls would grow and change depending on the choices made, as would the community around the space. As the player becomes more successful they could have the option to either opening up new spaces or trying to rebuild one of the other two initial options (if they picked a gallery, later they could purchase the theater or music hall).