Strategy consulting basically are the high end of consulting, people in the circle always consider McKinsey, Bain, BCG and BAH (big 4) as the genuine Strategy consulting firm, while a lot others claim they also provide strategy consulting solution, but they are viewed as tier-2.
In your case, if your top priority is to get in Strategy consulting firm like the big 4, you should seek to go HBS or Stanford or Kellogg, then you really have a bigger chance to get your foot in. but if you really don't want to go abroad, CEIBS has a track record in placing MBA in big 4, though very very few. but CKGSB never have graduates got in big 4 for the past years, in this regard, you should definitely choose CEIBS.