MIT has several distinct systems for reserving rooms. There's a whole bunch listed in the Event Planning Guide (most listed on
http://web.mit.edu/eventguide/other/independent.html; the big systems have their own pages linked from the sidebar or top bar on that page).

The two main groups of rooms (which are almost always what I've used, although Tech Squares has occasionally used some others) are:

• CAC spaces --- large event spaces (including La Sala). Those are reserved through CAC EMS (https://cac-ems2.mit.edu/EmsWebApp/) (as are DAPER (athletic) spaces). Generally speaking, CAC EMS will tell you actual availability and if you reserve the room online you have it. You need to know the username and password to use that system, but in practice you do *not* need to be on the reservation signatories list in the ASA DB (I think).
• Schedules spaces --- most classrooms. Those are reserved through http://web.mit.edu/registrar/classrooms/reserve/index.html. You can't see what rooms are available on that site, There's no username or password for that system; instead, Schedules will actually check Engage for authorization (at least, in theory, and I've seen a couple emails that suggest that they do in practice too).

Rooms We Reserve has some candidate rooms, mostly larger rooms suitable for Tuesdays, but the "Classrooms" section has a small list of smaller ones. The Workshop rooms page focuses more on smaller rooms.