https://www.ibisworld.com/us/industry/ohio/bars-nightclubs/1... (2025) estimates there are about 3,000 "bars and nightclubs" in Ohio.
And https://vinepair.com/articles/map-states-with-most-bars/ (2022) estimates there are 1800 bars in Ohio, apparently placing it in the Top 10 of states with the most bars.