The most recent study on World Cities by GAWC was in 2016 included the following American cities. They are listed in order from first place to last and divided into tiers.
http://www.lboro.ac.uk/gawc/world2016t.html
Alpha ++
New York City
Alpha
Chicago
Los Angeles
Alpha -
Washington, D.C.
San Francisco
Miami
Beta +
Boston
Atlanta
Dallas
Houston
Beta
Philadelphia
Beta -
Minneapolis
Denver
Seattle
St. Louis
San Diego
Gamma +
Cleveland
Detroit
San Jose
Gamma
Phoenix
Austin
Cincinnati
Kansas City
Tampa
Gamma -
Charlotte
Raleigh
Orlando
Columbus
Pittsburgh
High Sufficiency
Hartford
Milwaukee
Portland
Sacramento
Jacksonville
Indianapolis
San Antonio
Salt Lake City
Sufficiency
Richmond
Tulsa
Las Vegas
Memphis
Birmingham
Oklahoma City
New Orleans
Louisville
Omaha
Des Moines
Madison
Providence
Honolulu
Noticebly missing cities:
Nashville, Tucson, Albuquerque, and Charleston
Respectively, I'd argue that Nashville belongs in the Gamma - level and the other three are Sufficiency level. I can also quibble with some placements (San Antonio, Vegas, and New Orleans should be higher) based on my qualitative perception, but I have the vague impression these rankings are based on quantitative data, so I'll let the experts' opinions speak for themselves.