Map from Google - Busan

In Busan (or Pusan), Korea's second largest city, located on the southeast coast, the climate is temperate: winters are quite cold but sunny, and summers are hot, muggy and rainy, but tempered by the breezes. Like the rest of Korea, the city is affected by the monsoon circulation: in winter the northwest cold currents will prevail, while in summer they will be replaced by the hot and humid currents of tropical origin. Spring and autumn are transitional periods, mild and pleasant, especially the month of October.
Here are the average temperatures.
Average temperatures - Busan
Min (°C)-1051014182223191482
Max (°C)8913182224272926221610
Min (°F)303241505764727366574636
Max (°F)464855647275818479726150

In winter the average temperature is a few degrees above freezing (0 °C or 32 °F); there are quite mild periods, with highs around or even above 10 °C (50 °F), but also cold periods, and sometimes freezing. In the worst moments the temperature can drop to -10 °C (14 °F), or even below (though it goes better than in Seoul, where the temperature can get to -20 °C or -4 °F).
Busan is located in the least snowy area of Korea, that of the south-east coast: here snowfalls are very rare, and generally light.
Spring is mild, but the rains increase gradually. The rainiest season, however, is summer, because of the summer monsoon: from June to August, more than 700 millimetres (27.5 inches) of rain fall. The rains can sometimes be torrential. The worst month, the wettest and least sunny, is generally July. In summer there can be periods of good weather, which can be very hot, with highs about 35 °C (95 °F).
In autumn, rainfall decreases, and by October the rains are quite rare. Here is the average precipitation.
Average precipitation - Busan
Prec. (mm)4045851351552252602401656060251490
Prec. (in)

In August, September and early October (more rarely in July), Busan can be affected by typhoons, tropical cyclones of South-East Asia, which affect in a special way the southern coastal area, bringing torrential rain and strong winds, as happened with super-typhoon Sarah in September 1959, with typhoon Maemi in September 2003, and more recently with typhoon Sanba on the 17th of September 2012 and with typhoon Chaba on 4-5 October 2016.

Busan from above

The amount of sunshine in Busan is good in winter, when there are several sunny days, and reaches its minimum in July, when cloudy skies prevail (the sunshine amount goes down to 37%), because of the summer monsoon.

In Busan, and along the southern Korean coast, the sea becomes warm enough for swimming in August and September.
Sea temperature - Busan
Sea (°C)141313141720232624211916
Sea (°F)575555576368737975706661