You may begin with:

• Moody’s Analytics CRE - Search millions of real estate data points that cover every commercially zoned property in the U.S. Provides trend and forecast coverage across 10 major commercial real estate sectors, 275+ markets, and 3,000+ submarkets.  
• Real Capital Analytics (RCA)  Records over $40 trillion in commercial property transactions tied to 200,000+ investor and lender profiles, spanning diverse property types and global markets. Use the Transactions screen and filter by transaction details. Or use the trend tracker to find data on properties.
• Statista - quick statistics 
• Economist Intelligence Unit - time series on the topic by city worldwide. To begin a search,
  • select Data Tool
  • select All CityData 
  • choose city of interest
  • select Office and Residential Rents and choose appropriate options such as by sqf. etc.
  • select years
  • view data

Related sources: (might not be by city)

• Federal Reserve Economic Data, St Louis FED - scroll down to see data on US commercial real estate prices and real residential property prices. 
• Global Property Guide - data and articles by country
• US Department of Housing and Urban Development - datasets, surveys, articles on various topics of American housing