100 years from nothing (utter destruction) to disposable incomes, fairly large scale fermenting and the security to share a pint with mates.
It makes the cataclysm seem like an annoyance!
Hay a lot can happen in 100 years. Look how far we have come in the last hundred years. Besides 100 years is about 3-4 generations which would mean most people alive would only know of the appocalypse through stories from thier grandparents or great-grandparents.
Also it seems people are thinking of inns as if they are tourist stops. But really most in those times were simply resting stops for travelers going from one place to another. Even lands with bandits and thugs would have inns as they sometimes need a place to hang their hat and get a meal. They use fear and intimidation to keep the inn keeper quiet and most likely extorted money, food, and etc. from them. After all smart thugs know it's better to shack down a constant mark rather then simply kill them.
Not all inns were big like we think of hotels and motels today. Or the large city inns/taverns you see in the movies which are large enough to house to bar room fight scene as well as being large because they are in a city and have more customer. Many are more like the bed and breakfast type places you might find if you go traveling down the small roads and small towns across america.
Besides the size of the bar/inn the old westerns are also a great example of how lawless areas with thugs can still thrive somewhat. Even when rival gangs duke it out they tend to leave the inn keeper go since he's the one that can get them more food, beer, and so on. Plus there is the added bonus he cleans up their "hang out" after they smash it up.
Lastly they are natural meeting places because you can rest there was well as get food. They are often along routes that see a bit of traffic, otherwise they would have to close down. Thus people looking for passing merchants, passing mercenaries, or passing heroes in our case, hang out in the inns. And anytime there is a place people gather it creates commerce and thus they thrive.
In all honesty I think it makes sense that small inns and even shops would turn up fairly soon after the apocalypse as they would be centers of commerce. Either directly or indirectly by a more formal market place setting up right next to it.