Chicago is certainly more of a qualitative program. In recent years they have been trying to take a more pluralistic approach to methods and incorporate more quantitative methods, but they are particularly strong in qualitative methods. Off the top of my head they offer at least three courses in qualitative methods (Slater-comparative historical analysis, Wedeen-interpretive methods, and Mearsheimer-comparative case study).
You should also investigate Yale because they are particularly strong in ethnographic fieldwork. I know that they have at least one course on the topic and have a few faculty that write on the topic (lawrence, wood).
UCLA is also a qualitative-friendly program with courses in qualitative methods.
Plisar is correct about MIT.