Though UCSD has very strong China-oriented faculty portfolio, I would suggest MIA as it does not impose strict restrictions on China-related courses, which are on a much narrowly focused basis.
Based on my experience, having at least 4 Phd-Level general courses is a must. There was once a legend who took 6-7 Phd-level courses and ended in a top 15 econ program. To name a few, POLI 204, 220 (CP), 231 (Development), 232 (IO), 245 (IPE). Upper-number Q Method class like POLI 274 on text analysis will be of great help; I enrolled in a network analysis that they don't offer any more.
A few more comments on applying PhD in general:
1. Be prepared to be tortured.
2. Math and programing are really important.
3. Learn to lower your expectation. Every school has its strength and big-named ones are not necessarily the best.