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Indiana Memorial Union is a popular place. I know that APO makes good use of it and all sorts of other groups do too. They have rooms of all sizes, from small conference and meeting rooms to Alumni Hall, which has a capacity of 650 people. (We had our 80th Anniversary banquet in that room - it is huge!) Many groups, including APO, have offices in the Student Activities Tower at the IMU - this is handy for storing stuff! There are also rooms in the academic buildings that are used evenings and weekends (We used to have chapter meetings in one of the large lecture rooms in Jordan Hall, and we've met at the business school too.) Many of the dorms also have large multipurpose rooms - the Flame Room at McNutt is especially popular. There are also some restaurants and banquet facilities off campus.
There's definitely no lack of meeting or event space.