Here's a great post from @ninlive confirming the Dec. 29, 1989 date in Cleveland:
https://www.facebook.com/ninlivearch...e=3&permPage=1
Now, given that it lists Dec. 29, and not Dec. 28, I'm a bit skeptical of the 2-night run listed on a lot of sites. Nothing in the newspaper clippings indicates 2 nights. The date of that newspaper is Dec. 28, so it would have been extremely last minute if they'd "added a 2nd show due to demand".
This interview with NIN's tour manager lists the date as Dec. 28. But it may have been faulty memory from the manager or bad research from the writer. In any case, the manager's recollections make it sound like it was just one night, not 2 nights.
The origination of 2 dates comes from NIN Historian, and are based only on recollections. On NIN Tour History, no one has indicated that they attended Dec. 28. One person has said they attended Dec. 29. On setlist.fm, there is one person (HorrorShow) who is a troll, marking that he has attended nearly every show ever, so he is discounted. So, there is one person who said they attended Dec. 29. And one person who says they attended Dec. 28. For that person, they have both Dec. 28, 1989, and Dec. 28, 1990 (Hate Tour) marked as attended, so perhaps they only attended one date but marked both out of confusion because they weren't sure what year it was. And maybe the Dec. 28, 1990 show is the source of the Dec. 28, 1989 (if we assume this date didn't happen) confusion, with a faulty recollection about the year leading to a NIN Historian entry for that date also.
I'm mostly convinced that there was only one show on Dec. 29. The thing that would really solidify it for me would be a first-hand recollection about whether there was a set of two shows or just one.