inn: [OE] An inn was originally literally a place one lived or stayed ‘in’. It comes from a prehistoric Germanic *innam, which was a derivative of the ancestor of the modern English adverb in, and in Old English it meant simply ‘house where one lives, abode, home’. This sense survived into the 17th century (‘Queen Mary gave this House to Nicholas Heth, Archbishop of York, and his successors for ever, to be their Inne or Lodging for their Repair to London’, James Howell, Londinopolis 1657), and a memory of it remains in London’s Inns of Court, which originated as lodgings for lawyers.
The later sense ‘public house, tavern’ developed towards the end of the 14th century. => in
Old English inn "lodging, dwelling, house," probably from inne (adv.) "inside, within" (see in). Meaning "public house with lodging" is perhaps by c. 1200, certainly by c. 1400. Meaning "lodging house or residence for students" is early 13c. in Anglo-Latin, obsolete except in names of buildings that were so used (such as Inns of Court, mid-15c.).