Sounds like in terms of PTE, seems like you're leaning UVA and the cons of Georgetown seem pretty significant compared to UVA, so I'd go UVA.
Of your WL options, sounds like you really want to be in NYC and would thrive there, so best of luck getting into one of those. Of the two, sounds like Cornell might be a better fit for you than Columbia based on the culture and location within NYC, and you didn't mention this in your pros but there's also the fact that you mentioned you identify as queer and they have the Wellness Qlinic (nation's first LGBTQ+ mental health clinic) and you also mentioned being interested in refugee projects and health justice and Cornell also has the huge Center for Human Rights where they work with refugees and asylum seekers.