What cocktail is considered “unrefined” for someone to drink?

I’m writing a story where a pompous aristocratic character decides to indulge in what they view as “low quality” or “poor people’s” entertainment and they order an appropriately unrefined cocktail at a bar, but I don’t drink and don’t know much about alcohol. What drinks have this type of reputation? My first thought were rum and coke or a long island iced tea. Do these fit that description? What other drinks would work here?