World Cities Culture Report

London commissioned the World Cities Culture Report, which goes into great detail on the cultural aspects of what it thinks are the 12 greatest culture capitals in the world:  Berlin, Istanbul, Johannesburg, London, Mumbai, New York, Paris, Singapore, Sao Paulo, Shanghai, Sydney and Tokyo.

It is an interesting list.  I have focused more on economic aspects of cities.  If I were to add to it, I would suggest the following: 
Vienna ("The Historic centre of Vienna is rich in architectural ensembles, including Baroque castles and gardens, as well as the late-19th-century Ringstrasse lined with grand buildings, monuments and parks.")
Moscow, which has many art museums and performing arts.
Rome.  The eternal city.
Madrid.  Former capital of the Spanish empire.
San Francisco.  One of the best cities for tourism.
Hong Kong.  The most visited city on earth.
Dubai.  The most interesting city in the middle east.
Beijing. The second busiest airport in the world, and capital.

Honorable mention: Seoul, Stockholm, Toronto, Chicago, Mexico City, Abu Dhabi, Randstad, Boston, Rhine-Ruhr, Washington DC
Conspicuous by their absence: Osaka, Nagoya, Los Angeles, Houston, Philadelphia, Dallas, Atlanta