"The Tavern is the place where your folk celebrate your victories. A good feast is good income. Upgrade the Tavern so that more of your people can celebrate allowing you to increase your income."
A city can have up to 4 taverns. These are the places your villagers and knights alike can sit down for a drink, bringing in some extra money. Over time, taverns will accumulate gold up to their maximum hold. You can click on these taverns, whenever there is a floating coin above them, to collect however much gold they have made so far. Upgrading taverns (or building new ones) increases their gold income and the maximum amount they can hold before it needs collecting. You start off with a maximum of two taverns, and at throne room levels 3 and 5 you are able to construct another one.
To upgrade one tavern from 1 to 20, it will cost a total of 33,676,000 gold. For a single tavern to pay for the cost of its own upgrades, it will take 169 days (34 days with constant boosts), and 51 additional downtime-days spent upgrading. The graph below visualizes the cost vs. benefit scaling of taverns.
When considering the improved rate per level and the cost to upgrade to that rate, it is most efficient to put tavern upgrades at a lower priority when it reaches Level 13, until a player can afford to spend gold on Levels 14-16. Maximum benefit over cost occurs from Levels 10-12, and after Level 16.