It's not as much a "goth scene" as a "90's and later darkwave and bro-dustrial scene", but it's what we have.
As mentioned, there are two club nights (Church at Ace of Cups, and Cathedral at Spacebar) run by the same folks each month at two off-campus bars. Not exactly goth nights -- marketed as "Goth, Indstrl, Synth Aggro, EBM, DarkAlt and Classics". Lots of Faderhead and Assemblage 23, for example, with a handful of actual new/classic goth tracks mixed in (mostly fairly recent or covers). That said, they do attract a sizable crowd.
https://www.facebook.com/gothchurch
Those two monthly events, and pretty much anything that could be considered goth or goth-adjacent, will be posted in the Facebook group "Columbus, Ohio Goth Atmosphere for Dead Souls".
https://www.facebook.com/groups/788903001627368/
Another club night is Wake the Dead at Ruby Tuesdays (monthly), which plays fewer 'classics' and mostly newish/obscure darkwave. No Facebook page for some reason, but here's their upcoming event. Not super well attended, but a good option if you like that music.
https://www.facebook.com/events/150310407994277/
More to my taste is Vortex at Spacebar (monthly). Always classic 80's alternative, with a heavy dose of goth and deathrock. Recent theme nights have included an 80's goth night, an 80's industrial night, and even a Clan of Xymox night when they were in town. All vinyl, requests welcome.
https://www.facebook.com/vortexatspacebar
For other smaller regional events (Dayton, Cleveland, Cinci), another good resource is the Facebook group "Ohio Goth".