Yangyang (양양) is in Gangwon. It is a name of a small town and of a bigger county of which it is the capital.
Yangyang is a small coastal town (population: ~30,000) and a county in the very north east of South Korea in Gangwon province.
A number of buses leave from Seoul Express Bus Terminal daily, headed for Yangyang or Sokcho. Travel time on the tickets says 2 hours, but 3½-4 hours is more realistic (depending on traffic and weather conditions).
When buying a return ticket, this paper ticket might work only for the Seoul/Yangyang leg. Before departure back to Seoul, the ticket would then need to be exchanged at Yangyang Intercity Bus Terminal. (August 2020)
There are a few local buses (Line 9) that make the trip between the Yangyang bus station and the Naksan beach area, but they leave infrequently. A taxi ride for that trip takes around 5 minutes and costs around ₩8,000. (August 2020).
The gift store at Naksansa temple has some nice or interesting souvenirs.
And in the town there are several shops and stalls selling dried fish, squid, ...
The line of restaurants along Naksan Beach mostly offer dishes with raw fish. For solo travellers, Hoe-deop-bap (회덮밥) is a good meal choice.
In the street Naksan-sa-ro (낙산사로), also nearby, the focus is more on baked/grilled fish. If looking for a vegetarian main dish, quite delicious Deodeok-gui (더덕구이) can be found here, too.
It feels like the Naksan area of Yangyang consists almost entirely of "motels", all not-so-cheap with mediocre quality. If Korean is not a problem, it might be best to check out Korean websites and compare to find the best deal.
Primary administrative division