Here are county-to-county IRS migration data as represented on interactive maps via Forbes.
As readers of this page know, I worry about large-county (or large-area) aggregates. The variances for most measures are much too big.
USC's Cheng-yi Lin has fun playing with PUMS migration data. These areas are much smaller and their population density readings more useful.
Consider the top receiving (PUMS areas) PUMAs for MA+ (advanced degree) movers. They ended up in dense districts of Manhattan as well as in much less dense districts of Silicon Valley. In 2009, the #1 receiving PUMA for MA+ people (with MA degrees or higher; 12,537 arrivals) was in Manhattan with a population density of 44,799 residents per sq km. But the #2 receving area was in Silicon Valley (11,912 arrivals) at a place with a population density of 773 residents per sq km.
The density ratio of #1 vs #2 was a factor of 58 times.
For the top-50 receiving PUMAs, the average population density was 5877 per sq km, but the standard deviation was 8875; the coefficient of variation for population densities of the top fifty PUMAs was 1.51.
Witold Rybzcynski notes that metro area densities can denote many things, including suburbs where people meet and trade ideas.