My son is similar but not exact same as far as his background. We found schools that want to increase the % of Asian American and Asian students found his background as Asian American desirable. These are schools which actively recruit Asians/Asian American students and include them in their diversity fly in days (Bates, Bowdoin, Middlebury, andTrinity are some but there are others). I am not sure about Princeton as far as being Asian goes. I don’t think being Jewish helps or hurts at most schools. There are some which seem to have been trying to recruit Jewish students by having Kosher food and etc (or at least offer things that Jewish students might want/need to practice their religion). I personally believe that Asian Americans do have a harder time to get admitted to some schools and that these schools seem to keep a certain % of Asian American/Asians each year while schools in California that do not consider race at all in admission have huge percentages of Asians/Asian Americans. Some of this is likely due to location alone because there are high percentages of Asian Americans living in California. But I don’t think that explains all of it.
If you are listing yourself as multiracial, I am not so sure. I think that varies. Some schools do seem to want to increase multiracial students and mention it in literature. I think others would prefer students who are identified as Asian alone. I think there is possibly a general assumption that multiracial or biracial means black/white rather than the many other possibilities that exist.
Princeton is going to be hard for anyone to get into but some do every year and if it is the right school for you, I hope you get to go there. I would recommend applying to a range of colleges in terms of selectivity. Maybe check out some that actively recruit Asians/Asian Americans. It is very strange that Asians and Asian Americans often get counted as one group, by the way.