This map shows the town center (red) versus the weighted-center of population (blue). For example, Albany's Center of Population is farther east then the center of the city, while Bethlehem's Center of Population is north of center of the town.
 
I was interested in figuring out how to calculate this out after reading about the Census Bureau's Center of Population (https://www.census.gov/geographies/reference-files/time-series/geo/centers-population.html)
 
It's not difficult -- literally it's just a population weighted average of x and y coordinates of all the the tabulation blocks in each town.