inn (n.) Look up inn at Dictionary.com
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.).