Although Death Mountain has never been the most inviting place in Hyrule, as the volcano would often rain down flaming rocks upon a young Link in Ocarina of Time, its incarnation in Breath of the Wild is arguably even more deadly and lives up to its namesake. With a fiery environment that will easily burn Link to a crisp without the right equipment, it's easily one of the harder locations to navigate at the beginning of the game.
Once the player has progressed far enough through the volcano's region, they will find themselves in Goron City, a bustling, though somewhat-small town in the heart of the volcano. Armed with only his witts and a strong desire to not fall in the molten lava, Link will find many helpful items, merchants, and quests among the citizens of Goron City.
Merchants
Unless players have managed to get their hands on the Flamebreaker Armor on their way through the Southern Mine, found on the road towards Goron City, it is likely that their first stop will be at the Ripped and Shredded armor shop, where they can buy the full Flamebreaker Armor for a mere 3300 Rupees. If the player obtained the Flamebreaker Armor through the Fireproof Lizard Roundup side quest, then the cost will be 2700 Rupees instead.
There is also the Rollin' Inn, where Link can pay 20 Rupees to spend the night and heal all of his hearts back to full. Unlike other Inns, the Rollin' Inn has the option for Link to get a massage during the night rather than sleep in a more comfortable bed. The massage option costs 80 Rupees and will not only restore all of Link's hearts but will grant him 3 temporary hearts and one wheel of temporary stamina as well.
Goron City has its own general store run by a Goron named Tanko, the Goron Guston Shop, which sells a mix of different items including Fire and Ice Arrows, Rock Salt, Goron Spice, and Cane Sugar. While the arrows are useful in the surrounding areas, particularly the Ice Arrows, the Rock Salt isn't worth buying as they can be obtained fairly easily by breaking the many ore deposits found around Goron City.
Further towards the peak of Death Mountain, there is a communal cooking pot of sorts that is surrounded by several Goron and can be used to cook foods rather than using a normal-sized cooking pot. The Goron who runs the cooking area, Aji, also sells several food items, including Roasted Bass, Seared Steak, and Toasty Hylian Mushrooms. Finally, there is also a Goron named Offrak, found near the cooking pot, who will sell Link Fireproof Elixirs for 60 Rupees each and are useful if the player isn't able to obtain any of the Flamebreaker armor set just yet.
Loot and Korok Seeds
Goron City and its surrounding areas are fairly spread out, though what is contained within the city itself is actually fairly condensed. A Cobble Crusher can be found leaning up against one of the buildings, which respawns after every Blood Moon and is one of the materials needed to make Daruk's signature weapon, the Boulder Breaker, alongside 5 Flint and 1 Diamond.
While there are no Korok Seeds within the city walls, there are three that can be found in the immediate area, all of which being on the northern cliffside of Goron City. The first, which can be easily found by following the direction the bridge that heads north points up the cliff, which will be a Tree Stump Race that Link will have to complete in order to reveal the Korok. From this tree stump, there is a Korok to the east and west of this point, somewhat along the same ridge as this Korok. The western one is hiding inside the Goron carving's mouth, while the eastern one is hiding under a rock like most other Koroks.
Quests
Aside from the main quest to cleanse Vah Rudania of Calamity Ganon's influence, there are a handful of other quests that can be completed in and around Goron City. The most notable is the Captured Memories quest given to Link by Impa, as Pikango in Kakariko Village can send Link in the direction of one of these memories found in the Eldin region. Specifically, it is at the peak of one of the spires jutting out of the area around Goron City and can be fairly easy to miss without Pikango's guidance.
Greyson, one of the NPCs needed to progress through the From the Ground Up side quest to build Tarrey Town, can be found in Southern Mine, usually with a Goron child. In the same location, players can also find Kima, who is wearing the Flamebreaker Helm, and will give Link the Flamebreaker Armor in exchange for him catching 10 Fireproof Lizards. If players have obtained the Sheikah Armor, this process is much easier as the lizards are pretty skittish and will run as soon as Link spots them. For the most part, they are found hiding under rocks around the mine area and are fairly easy to grab once found.
One of the best side quests that players can finish if they are after a ton of Rupees is The Jewel Trade, which can be started by talking to the lone Gerudo in Goron City, Ramella. She will insist that Link bring her back 10 Amber and, in exchange, she gives the player 500 Rupees. However, this isn't the end of her trading, as she will take stacks of gems in exchange for more Rupees than players would otherwise get if they sold them in any other shop. Most notable, if players give her 10 Diamonds, she will pay 5500 Rupees, 500 more than what would be gained selling them elsewhere.
For significantly fewer Rupees, players can also talk to Fugo, who asks Link to kill the Ingeo Talus on Darunia Lake in order to impress his master. The easiest way to defeat an Igneo Talus is to load up on Ice Arrows at the Goron Guston Shop and shoot the Talus' weak spot with them. Not only will this deal a large chunk of damage, but it will also make cool them down to allow Link to climb on their backs and hit their weak spot up close. Once defeated, return to Fugo for a Silver Rupee.
Shrines
Like several other cities in Breath of the Wild, there is only one Shrine in the immediate area of the city to allow Link to fast travel back to. In this case, it is the Shae Mo'Sah Shrine, found on the highest point of Goron City, just before the path begins to lead further into Death Moutain. The Shrine puzzle involves a lot of fire and Bomb runes, as well as dealing with a handful of small Guardians in one particular room in the middle of the Shrine. There are several great items in this Shrine, including a Cobble Crusher, Ruby, and a bundle of 10 Ice Arrows found inside the chest, so making sure that nothing gets left behind should be a priority before leaving with the Spirit Orb.