Most events in J.R.R. Tolkien’s The Lord of the Rings take place in Middle-earth.
Middle-earth is the central continent of Tolkien’s invented world, Arda. The Lord of the Rings travels through many regions of it, including the Shire, Rivendell, Moria, Rohan, Gondor, Mordor, and the lands around the Anduin.
The name does not mean a planet or a separate universe in Tolkien’s original conception. It corresponds to the inhabited lands of a mythic version of Earth, and Tolkien connected the term to older Germanic and English expressions such as middangeard and Middle-earth.
Valinor and Aman are different places. Aman is the western continent, while Valinor is the land of the Valar within Aman. Númenor is another distinct island kingdom, destroyed before the main events of The Lord of the Rings.