It doesn't have any obvious meaning to me. If Giorgia says that's what it means in Italian, that's probably what it means in "English." It sounds like the hotel's own particular name for one specific facility. Personally, if I were booking a room at this hotel, I would check the hotel's website or I would call and ask about it when making the reservations. If the hotel is in the United States, they would not expect people to know the Italian word "taverna" and they would expect people to know the English word "tavern," so, yes, their guests would expect it to be some kind of bar, with some kind of Italian "atmosphere." For example, I find that the Statler Hotel in Ithaca, New York, features a "Taverna Banfi." In this particular case, at this particular hotel, the "Taverna Banfi is a truly unique Ithaca fine dining restaurant. Featuring alluring Tuscan ambiance and an energetic, enthusiastic staff, this welcoming bistro offers an enticing setting for private parties."

Taverna is an Italian word. In Italian it's a room with rustic furniture, with soft light. It can be a bar or a restaurant or a generic room when you can relax sitting on a armchair in front of a fireplace.

Probably a bar. But it isn't clear. The capital letters are a clue - that is a proper name, not a description.