Take a look at the Graduate School of Arts & Sciences website for all of your questions regarding housing, financials, life in New Haven, Student Organizations & more.
Here are some links to get you started:
Graduate School of Arts & Sciences https://gsas.yale.edu/
McDougal Center @ the Graduate Student Life Office https://gsas.yale.edu/life-yale/mcdougal-graduate-student-life-office
Graduate Student Organizations https://gsas.yale.edu/life-yale/graduate-student-organizations