Alpha order by continent, country and city
AUSTRALIA
Melbourne
Medical History Museum
http://www.chs.unimelb.edu.au/programs/jnmhu/museum
ASIA
HONG KONG
there is a new centre at Hong Kong University:
http://www.chm.hku.hk/index.html
SINGAPORE
(National University of Singapore) ARI (Asia Research Institute) has a cluster in STS including history of medicine.
TAIWAN
The research center for humanities and social sciences at Academia Sinica (Taiwan) has also a "Center for history of Health"