Following up on colleges which are need aware for international students, but do accept a good number of international students on aid:
Haverford (around 1/3 of their international students get financial aid)
Skidmore (similar)
Vassar (similar)
Trinity College (around 40% of their international students get aid)
Lafayette College (Around 1/2)
For these colleges, you are more likely to be in their top international applicants, so you are more likely to be accepted even if you are being considered as a need aware applicant.
In general, though, you should look at colleges which provide 100% need-based financial aid. However, since most are need aware for international students, you may want to focus on colleges at which you would be at the very top of their international applicants. So you look at their freshman profiles, and figure whether you would fit in the top students who were accepted.