Our campus is blessed with the presence of an establishment by the name of Round Table Pizza. A favorite of students from any department, it is the location of the approximately twice a quarter faculty/student mixers hosted by varying math faculty members.
Pizza is provided by the department, which guarantees the attendance of all but the busiest graduate students (or those who happen to have class or section during the event). As if that weren’t enough, Round Table also has many fine beers on tap.
It is a well-established fact that this helps break the ice for extended conversations between mathematicians. (Actually, we just made this fact up, but it seems plausible enough.)
In all seriousness, these events are an excellent chance to introduce oneself to and speak directly with faculty members, and much fun is always had by all.