Here are a couple ideas featuring prizes on the Change.gov Citizens Briefing Book site:
The Innovation Challenge - Some of the best ideas come from students attending our engineering and technical universities. Establish the "Best of the Best Inovation Challenge"that provides funding for research & development in three categories
1.)new energy solutions
2.) New environmental solutions
3.) Future Industryand Infrastructure innovation. ...
National Design Competition for Rebooting America - I would like to propose that the new administration sponsor a first-time ever national design competition as a part of the upcoming "rebooting of america". Architects, designers, artists and more could compete to dream up radical and optimistic ideas for restructuring America - such as making more social and safe urban living conditions, extremely energy efficient homes and neighborhoods, new small-scale urban structures to encourage more interactive neighborhoods with more shared resources, and even grader scale visions. ...