Red Dove Tavern
30 Castle St.
For something a little more classy and with more character, try the Red Dove Tavern.
Downtown Geneva is littered with local hangouts, some more holey-in-the-wall than others. This is part of the upstate charm.
Parker's
A local classic is Parker's, which has expanded into a small empire across across the region.
Stonecutter's Lodge the Belhurst Castle
For a nice night out, especially in cooler weather, try the Stonecutter's Lodge the Belhurst Castle. They often have live music and a fire going in the cobblestone fireplace, or one going outside in the firepit. And the wine is okay as well.
Note: all of these places also serve food. The writer does not recommend any of the straight up "bars" in Geneva. Leave that to the townies.