Disaggregated data on prices in US I have seen several papers that refer to the CPI Research Database, which contains micro-level data on prices in the US. For example, the data was used by Klenow and Kryvtsov (2005) and Nakamura and Steinsson (2007). 

The only similar thing I found is Average Price Data on the site of the Bureau of Labor Statistics. Unfortunately, this dataset is quite small. First, only food and fuel are presented there. Second, average consumer prices for food are available for the U.S. city average and four regions only. However, Nakamura and Steinsson (2007) write that prices of food are collected monthly in 87 areas.

So, there potentially is a more informative dataset which contains information on prices in all areas. 

Can I get it? What is the CPI Research Database? Is it available for the general public?
A paper published in 2009 by the Federal Reserve Board gave a brief description


  The BLS surveys about 85,000 items a month in its Commodities and Services Survey. Individual prices are collected at around 20,000 retail outlets across 45 large urban areas. The survey covers all goods and services other than shelter, or about 70 percent of the CPI based on BLS consumer expenditure weights. The CPI Research Database (hereafter CPI-RDB) maintained by the BLS Division of Price and Index Number Research contains all prices in the Commodities and Services Survey since January 1988. We use the CPI-RDB through May 2008, for a sample of "1988-2008".
  
  The BLS collects consumer prices monthly for food and fuel items in all areas. The BLS also collects prices monthly for all items in the three largest metropolitan areas (New York, Los Angeles, and Chicago). The BLS collects prices for items in other categories and other urban areas only bimonthly.


Details may have changed since then but essentially the database is an detailed dataset of prices for a wide range of selected items charged by a large sample of individual retailers at different points in time

It is not available to the public.  In particular, it contains commercially sensitive information about individual retailers

It is available to some academic researchers who reach an agreement with the Bureau of Labor Statistics putting restrictions on how they handle and how they use the database and on the locations where they access the data; BLS also charges a fee.  BLS provides details on Restricted Data Access on its website