Information on the C9 group of Chinese Universities can be found here.
There are a number of universities in Korea - links can be found here. Another option is Underwood International College, which is a college of Yonsei University. It offers a liberal arts curriculum.
Japan is broadening its programmes and many universities are offering programmes in English with the opportunity to also study Japanese. Examples include:
APU
Keio
Nagoya
Ritsumeikan
Tokyo
Waseda - SILS
These programmes often cost less than similar degrees elsewhere and also have merit scholarship opportunities.
Some major universities have campuses in Asia for example:
Monash (Australian) campus in Malaysia
Newcastle Medical School (UK) in Malaysia (a Newcastle degree)
RCSI (Ireland) Medical School in Malaysia
Temple (USA) University in Japan
RMIT (Australia) in Vietnam
NYU Shanghai (USA) in China
Duke Kunshan (USA) in Kunshan China
Nottingham Ningbo (UK) in Ningbo China