Three PC games to explore by setting and preference
Use setting to shortlist, then check the practical details.

Mafia: Definitive Edition, Red Dead Redemption 2 and Grand Theft Auto V Enhanced each have a PC Steam listing. Their supplied settings offer a useful first filter, although those details alone cannot establish which game will suit every player.
Mafia: Definitive Edition is a narrative crime game set in 1930s Lost Heaven, making it the clearest match here for someone specifically seeking that combination of period and subject. Red Dead Redemption 2 offers a Western setting. Grand Theft Auto V Enhanced places its setting in Los Santos and Blaine County.
Once a setting catches your interest, check the individual Steam listing. System requirements and controller support are listed by title, so assess each separately before purchase. This turns a thematic shortlist into a decision informed by your PC and preferred controls.