Thanks to the hard work of Erik Steiner and Jan Lahmeyer, the Spatial History Project has compiled what I believe is the most complete dataset on U.S. population figures over two centuries. The dataset tries to compile historical city populations decennially between 1790 and 2010 for cities above 2,500 people (when the U.S. Census Bureau first added them to their records), but the data is spottier for cities with populations below 2,500.
There’s more thorough documentation in the README about the sources for the data and method of compilation. We’ve placed the data on Github for use and improvement by others, so I hope you’ll check it out. Feel free to submit pull requests or get in touch with Erik or I with questions or suggestions.