Orlando, because as most of you have pointed out already, it is located in the center of the state.
Except it's not. The area centroid is west of Orlando, in Hernando County, and the population centroid is south of Orlando, in Polk County. Granted, it is closer to both centroids than Tallahassee is, tho Tallahassee is fairly close to where the population centroid was at the time Tallahassee was chosen to be capital.
I have always liked the idea of having the meeting place of Congress at the centroid of population. Dormitories could be built to house members of Congress during their annual sessions, not to exceed three months.
The White House could be turned over to The Smithsonian, National Park Service, or Marriot.