You learn that something strange is going on in Goron City, so you go to investigate.
Reach the Eldin Canyon Region
Go east from Lookout Landing and go straight at the first fork in the road, then go left at the next fork, so that you are going northeast. You will cross Rebonae Bridge, and you can optionally go south to Wetland Stable, and visit Tukarok Shrine nearby.
Take the road north from there, then turn right at the fork. When the path splits, go straight, and you will reach Thims Bridge. After that, go left at the fork in the road so you are going northwest. You will reach Woodland Stable, and you can visit Ekochiu Shrine nearby.
Go Toward Death Mountain
From the stable, you can optionally go east to Eldin Canyon Skyview Tower to map the region.
Then, from Ekochiu Shrine, go east on the road and it will lead you in the direction of Death Mountain. The path is straightforward for a while, then splits to the southeast and northwest. Go southeast first, where you can see Timawak shrine near Goronbi Lake.
Visit the Hot Spring
Goronbi Lake is a hot spring, so you can sit in it to restore your health, and you can drop bird eggs in it to boil them.
Visit the Bistro
If you go to the bistro on Goronbi Lake, you can talk to Mezer and Cook to start the side quest Meat for Meat.
Go to Goron City
Get back on the road and go northwest. At the split in the path, go right so that you are going northwest. At the next split, go left so that you are going north.
Eventually, you reach the gate to Goron City. You will be approached by two suspicious Gorons who offer to buy all of your ore for three rupees. Don't sell it. You can talk to Ramella afterward to start the side quest Amber Dealer.
Before you visit the quest destination for Regional Phenomena, you might want to visit Marakuguc Shrine, which is on the hill northeast of the village.