When the show ended, they publicly announced a plan to give the set to the Smithsonian. Ultimately, the Smithsonian rejected it because it was too big to store.
The set remained on a stage at Paramount for a few years as part of the studio tour.
Eventually they needed the space and donated it to the Hollywood Entertainment Museum.
I visited the museum a few times in 2002. On Monday nights they would have a catered "Monday Night Football" party.
Here are some pictures of me at one of those partys:
Yeah, I was having a Miller Lite on the Cheers Set.
The set was neat to look at. Lots of the props on the wall were simply pictures cut out of old newspapers and framed.