The hotel Bellosguardo is probably only fictional. Through the descriptions in the story one can extract that it is an upper class hotel.
As a matter of fact, there are two Italian towns called “Bellosguardo”, one in the region Compania and one in Florence. Both of them cannot be meant in the story because they are situated in the south or west, and Lydia and Mr. Gannett travel from Bologna further up to the north.