Wake Island was a tiny atoll located in Earth's Pacific Ocean, specifically in that region known as the Tropic of Cancer. It was near to the American state of Hawaii and the US territory of Midway Island.
Wake Island was not mentioned by name but can be seen fairly clearly on the map downloaded from the Enterprise computer in "The Cage". On the map, the island is indicated as "Wake I. (U.S.)"
Wake Island was an imporant theater during World War II. The Navy Expeditionary Medal (a decoration which can be seen worn by United States Navy personnel in Star Trek IV: The Voyage Home) was awarded for service on Wake Island.