I spent New Year's Eve in Montreal with some friends and we really didn't want to pay crazy prices just to sit at some cramped table. We ended up in Old Montreal for free and it was honestly the best night ever, seriously. The street vibe on the 31st is insane, tons of people, musicians everywhere, and you can bar hop without any commitment. If you want to grab a drink without paying through the nose, bring a bottle to someone's place before heading out - it costs way less than at a bar.
Parks like Mount Royal or Lafontaine Park also do free outdoor events on the 31st with music, entertainment, everything's free. You just gotta bring thermal layers because December in Montreal is freezing, but it's got a cool vibe and it's way less commercial than the tourist bars. You can also check out venues that do shows at reasonable prices - live music stuff, comedy, it's way cheaper than getting a table at a restaurant.
Another cool option is organizing something at someone's place. Potluck with a bunch of people, everyone brings drinks and food, you can stream an online party or put on some music - zero cover charge and it's usually way more fun than being packed into some dingy bar where you can't even hear each other talk. Honestly, on the 31st in Montreal you've gotta try the street parties instead of the spots that'll drain your wallet.