area, territory, sector

(ちいき) A zone or area. (emphasizes a social community moreso than a geographical area) (i.e. you wouldn’t use it for the tropics or the Arctic, but you’d use it for Chinatown, the American South or Kanto/Kansai). You’ll often see this on Neighborhood Watch signs.   $$$
(りょういき) A more general word for territory or domain – also used in neologisms like “domain name”.
(ちたい) A geographical district or zone – emphasizes a physical location:the tropics, the steppes. ちたい is much bigger and broader than 地域.
(ちく) A district of a city or town where a bunch of similar businesses are located:garment district, the diamond district, etc.
(ぶんや) An academic field.
(はんい) The scope or range of something. Police jurisdiction. The test covers chapters three through eight. Earthquake damaged an area from San Francisco to Redwood City. The manhunt covered the entire lower half of Manhattan.