Another thing that helps a reader believe in a tavern is if they sell believable stuff.
If there are cows in your world, there's a good chance that beef, steak, and dairy products will be common. Likewise the availability of chicken andf eggs and so on and so on. Taverns near the sea will probably seel a lot of fish or sea food.
When naming your drinks make them sound realistic, and have your characters order them realistically.
Wine and beer will always be popular, but dont make their names outrageous expositions of the diffences in culture between your fantasy world, and the real world.
Imagine how people order drinks in pubs or bars in real life.
In England, for example, people dont ask for "A pint of John Smiths Extra Smooth Cask Flow Bitter please", they ask for "a pint of smooth" or "A pint of Smiths' please" or if there's no other bitter on the bar "a pint of bitter".
Unless they are fairly snobby, most folk order; "large Cab-Sauv' please..." and rarely; "large glass of 1986 Hungarian cabernet sauvignon, Chateau Snooty Plonk please..." you might get that in a posh restaurant when ordering an expensive bottle, but rarely at the bar.
This particularly applies to regular patrons.
Taverns can really help you world build. Imagine one of your MC's has a favoutie beer, and struggles to find it outside of his home town, or region.
"We dont serve that Dwarf-**** round here!"
Plenty of off-plot mileage there.
Taverns are great!