The Graveyard Cave is just north of Hyrule Castle Town in Hyrule Field. You'll find it directly east of the Eternal Forest, south of Hebra Mountain, and west of Eastern Hyrule Field and Jabul Waters.
You can get there either by following the path north from Hyrule Castle Town, or by going east from Kakariko Village. There's a Smoothie Shop and a Waypoint close to the graveyard.
If this is your first time here, you'll notice there's a rift covering a large portion of the area. This is the Stilled Northern Sanctuary Rift, and you'll need to clear it to enter the Graveyard Cave.
Once the rift has been cleared — remember the Sanctuary for later if you want to get the best Echo in the game — head east towards a small graveyard. Speak to the lady who will talk about a hidden staircase in the graveyard, which you can find pretty easily.
Head up the stairs at the back to find a large gravestone with a brazier on either side of it. Use a fire-based Echo like Ignazol to light the torches, and the grave will move to reveal some stairs. Head down there.