Yes, millennials are moving to the urban cores but not in significant numbers when view from the context of larger city (metropolitan area) trends. That's the updated story, based on new small area data that approximates the year 2011 (Note: ACS 5-Year Data).
Small area trends are important to understanding developments in metropolitan areas, because conventional municipal jurisdiction based analysis obscures the extent of large suburban areas within the boundaries of most core municipalities. In 2010, approximately 58% of the population in core municipalities lived in small areas that were essentially suburban, with much lower population densities than areas that developed before World War II, and where nearly all motorized travel is by car. read more »