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?