It might seem that way too many adventures have began in inns, and taverns. In a way this is true. It can be overused as a starting point or the place where the adventurers meet for the first time.
On the other hand, where else would these vagrants meet each other?
Embrace the cliché. You don’t have to be unimaginative about it, however. Here’s some ideas.
Have a Character or the Characters Run the Place
Hey, if the place is such a hotbed of activity and the place to meet all sorts of unsavory personalities, why not just make it the centerpoint of the game. The PCs don’t even need to be adventurers in the usual sense. They don’t necessarily even need to leave the building (or buildings, if there are several). The inn itself can be enough of a hotbed of romance and intrigue to keep a campaign going for a while. Maybe the characters represent an outfit that is headquartered in an inn, like Al Swearengen. There they can hold meetings, defend against threats and eat well.
Perhaps the characters are becoming movers and shakers within their community because they have an inn that is a good place to hold discreet meetings between lovers, or just between conspirators. By cultivating trust with the powerful patrons, you can garner power for yourself.
Have the Characters Find Other Employment in Inns
Perhaps the characters are a troupe of entertainers, who move from inn to inn to find audiences. Depending on the players, they might enjoy this very much, putting on shows and LARPing them out as much as they want. Maybe there’s some other troupe they see as competitors, and end up meeting more than needed.
Perhaps the PCs are employed as merchants, who sell some special ware for the inns. The inns are probably pretty self-sufficient, and use local suppliers, but the better ones are going to want exotic spices and wines. Perhaps there’s room for entrepreneurs here.
Perhaps the PCs are conmen, who move from inn to inn, finding adventurers to sell forged healing potions, or whatever. That should have enough hazards to be interesting for a while. This could lead to the characters being pushed into heroics.
Have the Characters Be Brigands, Who Use the Inn for Intelligence
Who stops at inns? Besides all sorts of adventurers, you don’t really want to fight, because they don’t have any money to loot anyway, you have plenty on merchants, who are moving their wares from one point to another. Robbing one of them every once in a while (just enough not to draw the attention of any officials or discourage merchants from using this route) with enough planning should be fun. The innkeeper can be in on the deal (or one of the PCs).
Make Your Inn Fit Your World
If adventuring is an actual occupation in the world, the inns would probably react to that. If the inns have a very distinct group of people patronizing them, the inn would definitely try to serve them as best as they can. They could have their own blacksmiths on the premises, maybe sell food for the road and whatever else the PCs might need.
On the other hand, if adventuring and trade is rare, there might not be good inns anywhere. Perhaps there are only taverns that allow patrons to sleep on the premises if needed.
I would suggest you leave this to your players. Just ask them questions. What does the place look from the outside? The inside? What does it smell like? What does the ale taste like? What’s on the menu? Is there a lot of room? What’s the staff like? What’s written on the wall? What is that drunken person muttering about? Are there any sanitary facilities? What other services are provided (baths, prostitutes, stables, whatever)? Are there curious local laws that make the experience different (the barkeep asks some strange formal questions before serving, taxes, requirements about weapons, closing times, the house can’t accept coins from certain countries or mints, but has a separate business for exchanging them)? What mementos are there of earlier visitors?