We publish Case-Shiller Index numbers for 20 metro areas in a line chart that lets you compare the 20 cities. However, until now these have been the simple numbers published by S&P/Cotality. The chart has just been modified so you can see the effect of inflation on house prices in the same 20 cities.
You can find the chart here at cromfordreport.com, or here at our new site (under construction).
The original data is called “nominal” and represents the initial values. The control at the bottom of the chart allows you to choose either the National Consumer Price Index or the Phoenix Metro Consumer Price Index and apply this to the Case-Shiller Home Price Index.
Below is the chart using the HPI numbers for Phoenix using the CPI for Phoenix.

Adjusting for inflation increases index values for earlier dates because everything is converted to US dollars at their value in the most recent CPI release. This chart shows us that the peak of 2022 was not quite as extreme as 2006 and that homes are now 14% less expensive than they were in May 2022 and 17% less expensive than they were in December 2005.
It also shows that home prices adjusted for inflation have been falling slowly over the last 2 years. This is consistent with the Cromford Market Index being less than 90 for most of that period.
Among the other 19 cities, you will find many differing patterns for price behavior, so I encourage you to try the chart out for yourself. Atlanta, Boston, and Charlotte are the only metros among the 20 where it is reasonably valid to claim that homes are the most expensive they have ever been.