In the Prologue to The Lord of the Rings, Tolkien tells us that The Prancing Pony had been kept by the Butterbur family 'from time beyond record'. The fact that it had sections dedicated to Hobbits suggests that it probably didn't predate their arrival in those parts from around III 1050. The idea of the inn standing and remaining in use for some two thousand years seems rather implausible, but at least it seems to have been several centuries old by the time of the War of the Ring.