Before we get to where the center of the U.S. population is maybe we should say what it is. From the U.S. Census Bureau’s article The “Hart” of the Nation’s population: Hartville, Missouri (pop. 594) (11/165/2021):
Every decade since the first census in 1790, the Census Bureau has used data from each decennial census to calculate the center of population — the point where the country would balance perfectly on a flat map if everyone had the same weight of one.
In addition to a national center of population, the Census Bureau also calculates centers of population for each state, county, census tract and census block group. Coordinates for each of these locations can be found on the Centers of Population webpage.
The map here shows the center and how it has moved since 1790. This is near the bottom of the article and it is interactive in that users can choose individual states. The link in the quote will take users to a page with lat and lon for the mean and median centers of each state.