The geographic centre of the (edit: contiguous 48 states of the) US is a little north of a small burg called Lebanon, Kansas.

A Tsar Bomba at operational yield would be 100 megatons, or 7000 times the power of the bomb dropped on Hiroshima. The detonation altitude, chosen to cause the maximum amount of damage to domestic and light business buildings, would be about 14500 m.

The fireball would be 12 kilometres across, and would cause third-degree burns at 75 km from ground zero. The rapid expansion of the fireball would produce a shockwave that would destroy most buildings at 33 km from ground zero, and cause moderate to light damage out to 90 km. The shockwave would flatten Lebanon itself, and the other small towns nearby, while the thermal effects will likely cause fires to 75 km and beyond.

Fortunately, Kansas is not densely populated, so casualties would be much less than those of Hiroshima or Nagasaki, around 4000 dead, 30,000 injured. So far as I know, there are no strategic military assets in the area, so it would be a waste of a perfectly good bomb.

Edit: Alright, I concede! There are lots of things worth blowing up in Kansas!

Happy now?

The middle of the United States is between Kansas and Nebraska and a particularly low-developed sparsely populated area.

If detonated at the altitude of 14,500 meters for the max effect you can expect the blast radius of 92 km, with 96,000 affected, of them no more than 32,500 risking death or severe injury. Many more are risking the health effects of the radioactive fallout but it is hard to calculate, heavily depending on the weather at the time of the strike.

From the standpoint of the adversary of the United States in the conditions of the thermonuclear war, the best targets for the high-power munitions are LA Grand Park and Lafayette-Jersey St., Manhattan.

You can expect 64 million affected by the blast in one way or another, and just under 25,2 million dead and severely injured, not counting the effects of the fallout with just two detonations.

In that sense, targeting the center of the United States is rather wasteful for little effect. There are indeed legit high-value military targets not far to the northwest of the area in question.