As a furious roleplayer, taverns are very important andn unefortunately are really often missused in the video games. They are friendly places where you can meet the locals (yep, peasants...), have a drink, eat good fat food, sing, having s... sorry, fight, break everything, leave before paying the bill and escape the town guards.
I like the idea that getting drunk can get you throwing up, blured your vision, get you not walking straight can change your characteristics (- intel, + strengh).
I have some personnals ideas (some are mentionned above) like having hallucinations (you can fight ennemies and descover the day after that you killed 10 pigs and the farmer is angry). You can get "faked" quest that you should realize while you are drunk... there is a lot of possibilities and I trust Larian (that has shown that they like tu put some unusual things and funny hidden things that only a meticulous exploration can reveal) to do good things with that !!
Just a suggestion, in the game Fable (first of the name, not the 2 shitty things they released after) you have a list with some "succčs" like how many drinks you have, how many ennemis of each kind you killed, how many time you married, how many times you threw up... I think that it could be a funny idea to have such a funny list and as Larian like to develop his characters, they might put some hidden quest that you can unlock only by getting more famous among the populace or reaching a certain number of those "achievements"