1. Tokyo, Japan
--35th most livable city in the world according to the 2007 Mercer Human Resource Consulting Quality of Living Survey. Tokyo scored a 102.3 with the base score being 100.
--World's Largest metropolitan economy with a GDP (PPP) of USD$1.479 trillion.
--Considered one of the three world financial command centers along with New York City and London
--51 of the Fortune Global 500 companies are located in Tokyo more than any other city in the world.
--The Tokyo Stock Exchange is the 2nd largest in the world in terms of market capitalization and 4th in terms of share turnover.
--Tokyo International Airport is the 5th busiest airport in the world, handling 62,100,754 passengers in 2009.
--Tokyo has the 2nd highest cost of living of any city in the world according to Mercer's 2010 survey
2. Hong Kong
--GDP (PPP) of USD$293.11 billion
--Ranked freest economy in the world for 15 consecutive years by the Index of Economic Freedom.
--The Hong Kong Stock Exchange is the 6th largest in the world by market capitalization and is the largest IPO center in the world handling 22% of global IPOs in 2009.
--World's 11th largest trading entity. Hong Kong International Airport is the 13th busiest in the world by passenger traffic handling 45,560,888 passengers and 2nd busiest in the world by cargo traffic handling 3,384,765 tons of cargo in 2009.
--8th highest cost of living in the world according to the Mercer 2010 survey.
--71st highest quality of life ranking according to the 2007 Mercer survey. It received a score of 94.3 with the base score being 100.
--34th most livable city in the world according to the 2007 Mercer survey with a score of 102.5.
--GDP (PPP) of USD$239.966 billion
--The Port of Singapore is one of the 5 busiest in the world, handling 1.15 billion gross tons in 2005. It handled 29,918,000 containers in 2008 making it the world's busiest container port.
--The Singapore Exchange had a market capitalization of S$650 billion as of January 31, 2010
--Singapore Changi Airport is the 21st busiest in the world, handling 37,203,978 passengers in 2008
--It has the 11th highest cost of living in the world according to the 2010 Mercer survey.
--A.T. Kearney names Singapore the most globalized nation on earth in its Globalization Index.
I chose these three cities based upon the work of the GaWC Study Group of Loughborough University, UK. Their system rated the 60 most global cities in the "dimensions" of business activity, human capital, information exchange, cultural experience, and political engagement. In each dimension each city received a score of 1-60 (one being the highest possible score). Here is the GaWC data for Tokyo, Hong Kong, and Singapore. I will also include their data for Sydney, the highest ranked city in Oceania (seeing as you reference that region in your question).
Business Activity: 2
Human Capital: 6
Information Exchange: 7
Cultural Experience: 7
Political Engagement: 6
Overall Rank: 4th
Business Activity: 5
Human Capital: 5
Information Exchange: 6
Cultural Experience: 26
Political Engagement: 40
Overall Rank: 5th
Business Activity: 6
Human Capital: 7
Information Exchange: 15
Cultural Experience: 37
Political Engagement: 16
Overall Rank: 7th
Business Activity: 17
Human Capital: 8
Information Exchange: 27
Cultural Experience: 36
Political Engagement: 43
Overall Rank: 16th