I would pick Case.
Since you're an international student just a few pieces of information to remind you of (sorry if they seem overly obvious)
UVA is in a very rural area. It is a small college town. some people like that but many get bored of it. While it has gotten more diverse in the past couple decades it is still primarily not diverse.
Georgetown is in DC. It is a fun, friendly, lively city. I think it would be great for an international student. Georgetown undergrad is prestigious but the medical school is not as well ranked. I really like the school so I would maybe still consider it but I am not quite sure where your priorities lie. It will likely be one of your most expensive options. But it has a lot of great opportunities being that it is in DC.
Tulane is in New Orleans. It is a very fun city in the south - so a bit of a different vibe than Case for example - friendly and good food. Tulane has a lot of interesting infectious disease cases and public health problems. I think this would be a very interesting place to go. Again not quite as highly ranked as Case or UVA but I don't really think the differences in prestige in these schools are large enough to result in different career outcomes.
Case is in Cleveland. A lot of people think it is actually a really fun city for young people and has more opportunities than Charlottesville for example (where UVA is). Case is a really strong school that is why I picked it for you but really I don't think you can go wrong with your choices. I would say not UVA because I think you will be a bit less entertained and more isolated in Charlottesville. I would say Case if your most important factor is school rep. And I would say Georgetown or Tulane is you are most looking forward to living in a fun, fairly warm city (Tulane is warmer than Georgetown although Georgetown is still pretty mild in the winter). Tulane would get the edge if you are interested in infectious disease, global health, cardiovascular diseases, and Georgetown would get the bump if you were interested in health policy or orthopedic surgery in my eyes