Can anyone suggest a website (apart from college board and petersons) or a way to find schools that offer good financial aid to international students?
In general, I think the best aid to internationals is likely to come from well-endowed, highly selective private schools or else from schools that offer large merit scholarships automatically for qualifying stats. To have a good shot at most of these colleges, you may need to rank in the top 10% of your graduating class, with test scores >= 1400 (SAT R+M) or 31 (ACT composite), plus good course rigor, interesting ECs, and strong English language skills. If your qualifications aren’t so strong, and if your need is high, then you may be out of luck (in which case you might want to consider schools in another country).
The following Wiki page summarizes the need-based aid policies of many private colleges, including some policies/practices regarding international students:
https://en.wikipedia.org/wiki/Need-blind_admission
Very few are need-blind and also claim to meet full demonstrated need for internationals. However, as I interpret the Common Data Set information, colleges that claim to meet 100% of demonstrated need presumably do include admitted international students under that claim. About 60 colleges (many of them small LACs) claim to meet full demonstrated need.
Merit scholarships are a different matter.
Here is a list of schools that grant large merit scholarships automatically for qualifying stats (GPA, test scores):
http://automaticfulltuition.yolasite.com/
If any of those schools interest you, check their CDS files (section H) or their websites to make sure international students aren’t excluded. Many public universities do not grant any aid/scholarships at all to internationals.
This is a good site, but you need to research here, not ask others. Requests like this have been asked and answered many times.