The study "Real Wage Inequality" (published in the American Economic Journal: Applied Economics, 5 (1), 2013) by Enrico Moretti (Berkely) could be interesting for you.
A large literature has documented a significant increase in the return to college over the past 30 years. This increase is typically measured using nominal wages. I show that from 1980 to 2000, college graduates have increasingly concentrated in metropolitan areas that are characterized by a high cost of housing. This implies that college graduates are increasingly
exposed to a high cost of living and that the relative increase in their real wage may be smaller than the relative increase in their nominal wage. To measure the college premium in real terms, I deflate nominal wages using a new CPI that allows for changes in the cost of housing to vary across metropolitan areas and education groups. I find that half of the documented increase in the return to college between 1980 and 2000 disappears when I use real wages. [...]
Section 3.2 describes how to calculate local CPI using Census data from 1980, 1990 and 2000. I do not know whether the data is available (could find it neither on his site nor on the journal website) but I hope it still helps.
Added by LazarusL:
Some of the key points findings which relate to the question:
Using these two local CPI’s, I find that the level of the college premium is significantly
lower in real terms than in nominal terms. For example, in 2000 the conditional difference
between the wage of college graduates and of high school graduates is 60% in nominal terms
and only 37%-43% in real terms. Second, and most importantly, the increase in the college
premium between 1980 and 2000 in real terms is significantly smaller than the increase in
nominal terms. Specifically, the increase in nominal terms is 20 percentage points. The
increase in real terms is between 8 and 10 percentage points.
The author finds that the previous benefit of going to college in terms of increased wages is much smaller than the nominal wage differences make it appear, since many college graduates live in expensive cities where there incomes do not go as far in real terms.
The author also brings up other issues about whether people concerned with inequality should worry about real (adjusted for cost of living) vs nominal income.
The implications of this empirical finding for disparities in well-being depend on the
reasons for the increase in the share of college graduates in expensive cities. I consider
two broad classes of explanations. Under a demand pull hypothesis, the relative demand
of college graduates increases in expensive cities because of localized skill-biased technical
change or other demand shocks. In this case, college graduates move to expensive cities
because the jobs for college graduates are increasingly located in those cities, and not because
they particularly like living in those cities. The increase in their utility level is smaller
than the increase in their nominal wage due to higher cost of living. Under a supply push
hypothesis, the relative supply of college graduates increases in expensive cities because
college graduates are increasingly attracted by amenities located in those cities. The increase
in the cost of living in those cities reflects the attractiveness of the cities to skilled workers
and is the price for the consumption of desirable amenities.
Essentially, the author asks, are people going to expensive cities because that's where he jobs are (supply factors), or are the jobs in expensive cities because people want to live there (demand factors). The author finds that:
While I can not completely rule out that supply shocks may play a role, the weight of
the evidence seems consistent with the notion that a significant part of the variation in the
relative fraction of college graduates across cities is driven by demand factors.
So the empirical evidence he has indicates that jobs are in expensive cites mostly because people want to live in such cities. He does, however, admit that causation is a bit messy and he cannot rule out the possibility of supply factors.
Overall, this study does not give an in depth picture of the data for the entire US population with their incomes adjusted for cost of living, but it does give valuable insights into how cost of living effects inequality.