To find Goron City in The Legend of Zelda: Breath of the Wild, follow these detailed steps:

Step 1: Locate the Lanayru Tower
1. Activate the Lanayru Tower: If you haven’t already, activate the Lanayru Tower. This tower is located near Kakariko Village and can be reached by paragliding across the water to the north.

Step 2: Head North from the Lanayru Tower
2. Follow the Road: From the Lanayru Tower, head northward. You will see a road that leads northward on your map. Continue along this road until you reach a fork in the path.

Step 3: Take the Left Path
3. Take the Left Path: At the fork, take the left path toward the Maw of Death Mountain. This path will lead you closer to Goron City.

Step 4: Reach Foothill Stable
4. Arrive at Foothill Stable: Follow the pathway until you reach Foothill Stable. Here, you will find Gaile, who sells Fireproof Elixirs. It is recommended to buy three Fireproof Elixirs for 150 rupees as the road ahead can be treacherous.

Step 5: Prepare for the Journey
5. Visit Mo’a Keet Shrine: There is a Shrine located just southeast of Foothill Stable, the Mo’a Keet Shrine. It is a good idea to create a warp point here so you can easily return if needed.

Step 6: Navigate to Goron City
6. Head Towards Goron City: From Foothill Stable, continue northward. The pathway will lead you through the Southern Mine area. As you draw near Goron City, you will encounter a massive eruption causing flaming boulders to drop from the sky. Avoid the boulders and continue up towards Goron City.

Step 7: Enter Goron City
7. Arrive at Goron City: Once you arrive at Goron City, you will see a cut-scene of the Divine Beast tormenting Death Mountain, causing the eruptions. The city is home to the Goron people, led by their Boss. You can look around as you please, but then make your way to the target on the map to speak with Bludo, the Goron Boss.

Optional: Acquire Flamebreaker Armor
8. Acquire Flamebreaker Armor: If you want to avoid bursting into flames, you can purchase flame-resistant armor from Rogaro at Ripped and Shredded, the armor shop in Goron City. The Flamebreaker Boots, Armor, and Helm provide flame guard, allowing you to stay in Goron City without catching fire.

By following these steps, you will be able to safely navigate to and explore Goron City in The Legend of Zelda: Breath of the Wild.