Here is my personal list of classes that I am taking and my reasons why. Yes, in my opinion, being a well rounded doctor also means a lot of social sciences and humanities. It's not just science classes and medically related courses.
1) Language classes -- knowing another language will only help you.
2) Sociology classes -- while we must appreciate how far society has progressed, we must also understand the challenges we still need to overcome. Analyzing institutional structures and ideological formations is crucial. Race, gender, class, sexual orientation, etc. - their impacts on how a person struggles in society, their coalescing effects when together (the struggles that a Hispanic woman may face that a White woman or a Hispanic male may not face), and what progress still needs to be made are all things that everyone needs to know, especially a physician who will most likely treat all types of people.
3) Psychology classes -- Understanding how a person thinks, why they think in that way, and what led them to this sort of thinking can help you better empathize and sympathize with patients. I highly recommend developmental and social psychology classes.
4) History classes -- particularly relating to US history, it may be helpful to know the history of different minority groups and the challenges they've had to face. That helps you appreciate the different struggles that they still face today. Knowing about our country also never hurt anyone.
I'm sure there are plenty more classes that can help you become a more well rounded doctor, but these are a few (IN MY OWN OPINION) that will help you, if not become a more well rounded doctor, at least become a more well rounded person and informed citizen.