The Lord of the Rings takes place in Middle-earth, a world invented by the writer J.R.R. Tolkien. Peter Jackson filmed it in more than a hundred places in New Zealand, from sheep farms to volcanoes. Start at the Hobbiton Movie Set, the village of the hobbits, which is still standing and open on guided tours. Many other places were empty landscapes: no set is left, but the view is the one you know from the films.
New Zealand is long, so plan one island at a time. On the North Island, Wellington is the base: Mount Victoria above the city, Rivendell in Kaitoke Regional Park and the Paths of the Dead at the Putangirua Pinnacles, with Mount Ngauruhoe, the real Mount Doom, on the way from Auckland. On the South Island, Queenstown is the base: the Arrow River in Arrowtown, the Kawarau Gorge and Paradise near Glenorchy are all within an hour, while Mount Sunday, the hill of Edoras, is a longer drive.
Check before you go: Hobbiton and the Pelennor Fields can only be visited on a tour, Deer Park Heights needs an entry code bought ahead, and mountain walks depend on the weather. You need a car for almost everything. Bilbo's adventure, sixty years earlier, has its own page: The Hobbit.