I thought that map represented several students from China (comparable to the number at Kenyon). But on second look I think you’re right, it is only showing one pin per represented country. So we really don’t know how many Chinese students are at Williams. We also don’t know their admission rate or average stats.
Nor do we know the qualifications of the OP’s kid. I don’t doubt that it is challenging for almost any Chinese student to get an admission and acceptable aid offer from a selective American college. I think the question is where to look for good schools where the odds are at least a little higher than the Ivies and other relatively well-known, top colleges. That’s the question the OP is asking, isn’t it?
Skidmore College is much less selective overall than Williams. For 2014-15 it awarded financial aid to 96 undergraduates, averaging $56,600 per award. If anyone knows how many Chinese students are at Skidmore, I’d be interested in those numbers.
Macalester’s overall admission yield is ~24%.
If ~15 Chinese students are enrolled per class, and if the Chinese yield rate is about the same as the overall yield rate, then Mac must be accepting about 60 of the ~300 Chinese students who apply. So the Chinese student admission rate would appear to be about 20%, or about half the overall admission rate. That’s very competitive, but not hopeless. USNWR ranks Macalester #23 among National LACs. For 2014-15, Macalester awarded financial aid to 215 international students, with an average dollar amount of $42,377 per award.