The Earth's core is the interior of Earth.
During season 3 of the 1987 TV series, the Technodrome is located in a very unrealistically portrayed version of the Earth's core, following the Ninja Turtles sending it there at the end of "Return of the Technodrome". The Technodrome seems able to stand the magma and extreme heat. In the episode "The Missing Map", Zach is about to fall out of an open hatch and out of the Technodrome, into the magma, but manages to grab a railing at the end.
Throughout season 3, Shredder, Krang, Bebop and Rocksteady rely on Transport Modules to move between the Technodrome and Earth's core. In the Big Trilogy, the Technodrome finally resurfaces before the Ninja Turtles send it to Dimension X.
In Eastman and Laird's Teenage Mutant Ninja Turtles, volume 2, during the DARPA mission towards the end of the volume, there is a Triceraton asteroid ship that has been en route since ever since the Ninja Turtles' appearance and escape from "The Triceraton Homeworld" in volume 1. By the time it nears Earth, the ship is in a dilapidated ship and many of its personnel have died. The ship's Triceraton forces launch an assault on DARPA in Nevada where their long missing Triceraton compatriot has been located. But with the battle going poorly for the Triceraton side, the asteroid ship stages one last suicide run to collide into the Earth at DARPA's location at high speed to kill as many of their enemy as possible—to a Triceraton, this is considered an honorable death in battle. But Louis Braunze and his friend, the only surviving alien of the group the Turtles had previously freed from DARPA imprisonment, use the inter-phasic cannon, a piece of alien technology that DARPA had seized, to temporarily force the Triceraton asteroid ship out of phase with surrounding space. Instead of colliding with the Earth, it travels harmlessly through the Earth's surface, and comes back into phase inside the Earth's core where the entire asteroid ship is instantly destroyed.