From Tolkien Gateway

The Mathom-house was a museum-like building in Michel Delving where the Hobbits collected and displayed "mathoms": items and trinkets for which they had no particular use. It was known to contain a store of weapons,[1] and for a time also (between T.A. 2941 and T.A. 3001) it held Bilbo Baggins' mithril coat.[2][3]

Portrayal in adaptations[edit]

2007: The Lord of the Rings Online:

The Mathom-house is the place where players can turn in reputation items to gain favour with "The Mathom Society", the main reputation faction for the Hobbits of The Shire, which is situated here.