Don't just rely on public listings. Check your alma mater's listservs or job announcements, these often prioritize you and sometimes these openings are never publicly advertised.
Also check lab websites. Do this through the graduate or MD/PHD faculty page, as the links are often there. Sometimes openings are listed, and cold email labs you especially like. Sloan Kettering, Weil Cornell, Rockefeller, and NYU are some good schools in that area. Good luck.