Here's what I found thus far, courtesy of RadioDiscussions.com:

Baltimore/DC/Lancaster (https://www.radiodiscussions.com/threads/retro-baltimore-dc-lancaster-saturday-october-20-1990.702932/post-6155927), 5 - WTTG (FOX)

Chicago (https://www.radiodiscussions.com/threads/retro-chicago-sunday-january-27-1991.714932/post-6241554), 32 WFLD (Fox)

Eastern North Carolina (https://www.radiodiscussions.com/threads/retro-eastern-north-carolina-sat-july-27-1991.586777/), WFXI 8-Fox; WKFT 40-Ind

New York [Metro] (https://www.radiodiscussions.com/threads/retro-new-york-metro-saturday-january-5-1991.714489/post-6238224), 5 WNYW (Fox)

North Carolina (https://www.radiodiscussions.com/threads/retro-north-carolina-9-14-91.444908/), 45 WNRW (Fox)

Pittsburgh/Ohio & Mahoning (https://www.radiodiscussions.com/threads/retro-pittsburgh-ohio-mahoning-valleys-sat-may-18-1991.647601/post-5865619), WPTT 22-Ind

Yakima (https://www.radiodiscussions.com/threads/who-aired-what-where-lesser-known-syndicated-shows.667301/post-6125053), K53CY, 1PM Sun


In Los Angeles (https://www.latimes.com/archives/la-xpm-1990-09-29-ca-1059-story.html), it aired on KTLA 5.

According to this blog (http://thelandofwhatever.blogspot.com/2020/09/forgotten-tv-what-dummy-1990.html), some stations that had the rights also were network affiliates and had commitments to sports (i.e. college football), meaning that What a Dummy, depending on where you lived, didn't have a steady time slot.