Gyeongju, another nearby city is mostly known for historical tourism and home to some incredible living UNESCO sites. But not much else since it was the capital of a now defunct nation in the 900s. Busan is the second largest city in South Korea and one of the few cities that made it through the Korean War without being flattened into rubble and who's principal industry is port logistics and fishing -- it's basically Singapore or Hong Kong of South Korea without all the financial business.
Ulsan is very much a company town on who's fate rests Hyundai's successes -- and Hyundai hasn't been killing it recently. The city is also home to the world's largest auto factory and number of other Hyundai conglomerate sites. As Hyundai's fate twists and turns in the global winds, so does the entire city. It doesn't have much to do with the other nearby cities, and it's on the northern edge of an isolated region that's politically aligned with the ruling party, while the rest of the region it and Busan exist within voted for the other guy.
The relationship with China has been rockier than I think anybody has let on to and historic relations with Japan have never been exactly "warm". The recent THAAD anti-missile situation really rattled the Korean-Chinese relationship and between turning the Chinese public away from obviously South Korean goods in bulk numbers, China has also seriously ramped up ship manufacturing and I believe now leads in total tonnage.
In addition, new shipyards are coming online in India and Vietnam putting additional downwards economic pressure on these three shipyards that used to enjoy a near monopoly. Even worse, global shipping hasn't recovered, and movement of energy products (oil and gas) is geographically shifting (less oil needing to move from Saudi to the U.S. for example) so demand for ships is down, AND several large shipping companies went out of business putting more ships up on the secondary market AND it turns out very very very large ships didn't work out as well as was hoped, so orders for that equipment never materialized.
As for the other major business there, Korea's auto manufacturing business has also been consolidating and changing. Hyundai is the major manufacturer, but Hyundai-Kia has moved much of their manufacturing overseas from Korea into the domestic markets they sell into and the rest of the auto industry in Korea is in disarray and succumbing to foreign manufacturers finally clearing various import hurdles and selling in larger and larger numbers. Among the "basically defunct": Daewoo Motors (now GM), Samsung Motors (now majority owned by Renault), SsangYong Motors (now owned by Mahindra). Some of these are still large, but dying giants.
It looks pretty bad to be honest and my guess is that Ulsan may soon turn into South Korea's Detroit.
Here's a pretty good article that outlines some of these problems in terms of raw tonnage https://wolfstreet.com/2018/07/07/big-three-korean-shipbuild...