This is one of the few things that really bother me in medieval style games. Taverns were one of the few, if not only, social place in that time besides the church.
People came there to forget work, relax, tell stories, drink, hear music and news, sadly it gets so little attention in games.
DA:O did have a lot of things that you expect in a tavern, music, games etc but they did nothing with it, it was just background and it was always the same, always the same people, same conversation, same music
I really liked the taverns in The Witcher, you could roll dice, fistfight, armwrestle and it changed, because of the day/night cycles you saw people coming and going etc, plus, you could actually get into drinking contests and get drunk
Same in Skyrim, more natural interactions, people walking around, music on request, maybe not the best singers but imo thats a good thing, that is realistic, the best singers would be in royal palaces etc, not in a tavern.