The 'Most liberal American cities' are so-called "progressive" cities in the United States that are usually are in Blue states / unfree states.
These most leftist cities typically have even more draconian Nanny state local laws in addition to the onerous liberal state laws in support of the progressive police state, especially support for Gun free zones, Gun control and ammunition control, along with the Homosexual agenda (see San Francisco values), and illegal immigration "sanctuary" and tend to follow Hollywood values in terms of drugs and other liberal values.
Liberal Cities Generally Found in "Unfree States"
Almost all of the liberal cities, with the exception of Austin, Texas, are found in the the Blue state liberal Democrat "death spiral" Nanny states / progressive Police states. "The East Coast and West Coast (Left Coast) had the most liberal states including Vermont, Massachusetts, Delaware, New York, Hawaii, Oregon, Washington, Maine, California and New Jersey." 
Phil Reiff, Director of the liberal Bay Area Center for Voting Research says, "While there are a few liberal cities without large African American populations, these wind up being the exceptions. The list of Americas most liberal cities is dominated by cities with large African American populations that are concentrated in the Northeast, Midwest and California."
Americas Most Liberal Cities (in descending order)
1. Detroit, Michigan - see Bankruptcy
2. Gary, Indiana
3. Berkeley, California - see Professor values
4. Washington, D.C.
5. Oakland, California - see Black Panthers
6. Inglewood, California
7. Newark, New Jersey
8. Cambridge, Massachusetts - see Professor values
9. San Francisco, California - see San Francisco values
10. Flint, Michigan - see Michael Moore
11. Cleveland, Ohio - see Dennis Kucinich
12. Hartford, Connecticut
13. Paterson, New Jersey
14. Baltimore, Maryland
15. New Haven, Connecticut
16. Seattle, Washington - see Bill Gates and Steve Ballmer of liberal Microsoft
17. Chicago, Illinois - see Obama and Rahm Emanuel
18. Philadelphia, Pennsylvania
19. Birmingham, Alabama
20. St. Louis, Missouri - see Ferguson, Missouri Michael Brown
21. New York City, New York - see Michael Bloomberg
22. Providence, Rhode Island
23. Minneapolis, Minnesota
24. Boston, Massachusetts
25. Buffalo, New York
26. Madison, Wisconsin - see Professor values
27. Austin, Texas
28. Hollywood, California - see Hollywood values
29. Los Angeles, California
30. Portland, Oregon