Pay off the 20% of the national debt with the highest interest rate, just so everyone would shut up about it for a minute.
Set up a $1 trillion dollar prize for a clean, renewable energy source. $100 billion for a viable proof of concept and the rest doled out as the tech is implemented worldwide.
Another $2 trillion in grants for infrastructure improvement in America. $2 trillion for the rest of the world. Major focus on high-speed Internet and other forms of data transmission. Another $1 trillion to educational institutions, with an emphasis on vocational training and medical schools.
$100 billion endowment to the Boston Celtics with the mission statement "shoving it in the Laker's faces." and a brief elastic clause of "interpret that however you want, just don't screw it up."
That'd leave around a trillion for me. I'd probably spend a lot of it on loose cars, fast women, overpriced booze, and random, pointless trips to space. The rest I'd just waste.