Well there is the primary care rotation, which as well as in new york can be done at the Bronx VA as part of a 3 month longitudinal rotation, rural parts of neighboring states, and also via the indian health services rotation in new mexico and arizona. I did the latter and it was the best experience of my clinical year. There are certainly lots of opportunities to work with the underserved in Harlem and Washington Heights. I did CoSMO for 5 years, but similar experiences can be obtained via CHAMP (Harlem Homeless) and Curhon (High risk individuals such as IV drug users and domestic violence victims). We also have a program through Amnesty International or a similar group that provides histories and physicals for people seeking asylum on the grounds of torture.
Plenty of options for global health, including paid experiences or those that pay for travel at least. We have affiliates in about 30 hospitals in 21 or so countries off the bat. You can also do your scholarly project abroad, and are allowed to be abroad for up to 6-7 months total during your fourth year.
I was drawn by the culture of diversity of interests in and out of medicine. I also liked the way that everything was flexible (non mandatory lectures, pass fail unranked, almost entirely elective 4th year, etc). It's a culture dedicated to allowing for people to find their own path. The value of p/f unranked is that it gives you the confidence to chose when you've mastered the material and move on to utilize the many other opportunities available at Columbia (be it research, volunteering, exploring NYC, etc).
It is very easy as a medical student to get involved in research, and I can't really claim that this is Columbia specific. Columbia has a strong core alumni group, and this breeds a lot of camaraderie amongst the students and residents/faculty. Columbia also does not require professors to teach as part of tenure. Everyone is a volunteer. This doesn't necessarily mean that all volunteers are good teachers, but it does mean that they genuinely are committed to your education. If you are willing to put in the effort, it is easy to publish something during medical school. I dealt with clinical research mostly. As a aside, the scholarly project doesn't have to be research. It can be public health, international, or even artistically inclined. One of my classmates did sketched collages depicting patients in and out of the hospital (with consent obviously).
The unique opportunity I recommend exploring at Columbia is the fact that you can take 2 classes per semester at any school or department at the university absolutely free (Law is the one exception). Thanks to the p/f curriculum, it isn't stressful to do so even.