Public parking is available near Con Ja Nai in a few locations. You will want to check the Downtown Development Authority’s site for more detailed information.

Parking in University of Michigan lots is generally not allowed, unless there is special event parking or enforcement is suspended. The University’s parking website is a little confusing, but does have enforcement information. On Saturdays, the following lots on the Medical Campus (northeast of the MLB and require crossing the major thoroughfare Huron St.) are free for public parking: Catherine (M5), Glen (M61), Ann (M86), but are quite a bit further than the lots mentioned below.

Liberty Square is closest to CJN, and is $1.50/hr. However, there is construction on Washington St. between the structure and State St., so plan your route accordingly. For long-time CJN attendees, please note that the $5 all day parking on Saturday is no longer available.
The Maynard structure is also $1.50/hr, relatively close to CJN.

The map below shows those two parking structures and their relative position to Con Ja Nai. Liberty Square is north of the Maynard structure. Click for full view.
As a note, Thayer (N4) that is marked in blue next to the Modern Languages Building, will be open to the public for $10 after 2pm due to a nearby concert that evening.