I have a bunch of gyroids in mine, because I would never be able to remember what each one looks/sounds like otherwise. I have them in rows all turned off, so I can pick them out from there easier.
I'm currently making a little cafe and spa room for my villagers in the museum. Usually, they're used as storage, but I had too mny decor ideas and decided to do it in the museum as well.
Mine are empty. I've never been a hoarder, I usually sell stuff I don't need and only keep some harder to obtain unorderables. I've never thought about simply displaying things in the museum. It could be a fun place to put my favourite sets that I have no use for, I guess. I don't think I'd go to great lengths to make it look amazing though, museums never really get visits from other players.