As others have mentioned, this is actually three museums in one, housed in the former palace of the bishops/cardinals. Each museum is located on one floor, the archaology museum in the basement, museum of decorative arts on the ground floor, and museum of fine arts on the upper level. You can buy separate tickets, but the three together were only 12 euro. Each museum was interesting in its own right. Archaeology museum showed the history of the area from pre-historic times, through Roman, and more recent. Decorative arts were mostly rooms of the palace as they would have been, along with rooms showing porcelain, gold work, etc. Museum of fine arts had a variety of paintings, and during my visit a special exhibition on Jean-Jacques Henner.
My one complaint is that flow in each of the museums was a little confusing. Some rooms had multiple entrances/exits, and it wasn't always clear what route you were supposed to take to ensure you were seeing everything.