Wandering in from Network: For an establishment that mostly provides the mid-day meal to working-class people on their lunch break, the most common late-19th century equivalent would probably be "Lunch counter" or "free lunch counter". Free lunch counters did in fact serve alcohol - you got free lunch (usually a quite elaborate one) in exchange for buying overpriced drinks. But this was the stereotypical working man's lunch pretty much until Prohibition. Lunch counters, serving the same clientele but more likely to have respectable women in them and mostly non-alcoholic, also appeared in dimestores and low-end department stores around the same time.

"Diner", "Cafeteria" and "Cafe" also showed up in the late 19th century with pretty much the same meanings they currently have in English.

Earlier in the 19th century I'm not sure! There would have been pubs/saloons/taverns/pubs/bars that served meals; and also coffeehouses going back to the Colonial period, though they would have been more middle-class; higher-class restaurants in hotels; and street carts selling food.

In cities along the East Coast there would have been lots of oyster bars or raw bars, usually serving mostly cheap beer and fresh shellfish (and maybe a few other seafood-y dishes). That was also a very working-class thing. (Apparently "Oyster bar" only came in about 1870 and they were "oyster houses" before that.)