According to the legend, Loreley (this is the preferred spelling in German) sat on top of the Loreley Rock (Loreleyfelsen, or just Loreley), an eye-catching 133m (400 feet) high slate rock above the city of St. Goarshausen, situated in a rather sharp bend of the Rhine river. The bronze statue of Loreley is not on the top of the Loreley Rock but on the mole of the harbor of St. Goarshausen.
The etymology of the name "Loreley" or "Lorelei" is disputed. While lei is an obsolete word for "slate rock", lore is said to either be derived from Middle High German lûre "look-out" (Lauer in modern German) or related to "Laura", a name for Holda, the Germanic goddess of winter (IMHO, the first explanation makes more sense).
The view from the top of the Loreley Rock is splendid but if you don't have the time for the trip you can also see the rock from below, from the window of one of the many trains that run past it on the opposite bank of the river, such as the Intercity between Koblenz and Mainz (it comes between two tunnels; if you want to take a picture you have to be prepared).
There is an open-air theater on the rock plateau above St. Goarshausen, where opera performances and rock concerts are held during the summer months.