The obvious benefit is giving NASA a more inspiring mission than being an errand boy for the academics who their little experiments in orbit. Sun Tzu teaches that organizations need a meaningful mission to unite and focus them. Without a mission, NASA is just another disaster waiting to happen. Astronauts are no longer space explorers needing "the right stuff," but ferry captains.
What makes the plan truly strategic is that it uses Sun Tzu's concept of positioning. First, it establishes a base on the moon to acts as a forward position for approaching Mars. Then it uses Mars as a forward position for exploring the rest of the Solar System. Each step is small and incremental. Like true progress and unlike the space race, there is no endpoint.
Of course, I have already said I like the political leverage it provides. As long as the Rover's are roaming around Mars between now and the elections, Bush's proposal is going to get press attention. Democrats will attack, saying the money is better spent on the disadvantaged, but that is the Democrat response to everything. More importantly, the Democrats will have to respond. They will have to attack Bush on this because they have to be against everything Bush.