Map from Google - Incheon

In Incheon, a Korean city, located in the northwest of the country, on the coast of the Yellow Sea and a short distance from the capital Seoul, the climate is continental: winters are very cold but sunny, and summers are hot, sultry and rainy, though tempered by the breeze. Like the rest of Korea, the city is affected by the monsoon circulation: in winter the northwest cold currents prevail, while in summer they are replaced by hot and humid currents of tropical origin. Spring and autumn are transitional periods, mild and pleasant, especially the month of October.
The climate is very similar to that of Seoul, although it is a bit milder (less cold in winter, less hot but more humid in summer), and less rainy, because of the location on the coast. For example, in January 2011, in Seoul the temperature dropped down to -18 °C (0 °F), and in Incheon to -15 °C (5 °F); in January 2016 it dropped to -18 °C (0 °F) in Seoul and to -16 °C (3 °F) in Incheon; in August 2016 it reached 36.6 °C (98 °F) in Seoul and 34 °C (93 °F) in Incheon.
Here are the average temperatures.
Average temperatures - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDec
IncheonJFMAMJJASOND
Min (°C)-5-3281318222218114-3
Max (°C)241016212528292620125
Min (°F)232736465564727264523927
Max (°F)363950617077828479685441

In winter the average temperature is around freezing (0 °C or 32 °F) or a few degrees below; sunshine is quite common, and a cold wind often blows from the Asian continent. On colder periods, the temperature remains below freezing during the day; in the worst moments it can drop to -15 °C (5 °F) or below.
Although winter is a dry season, sometimes it can snow.
In winter, and especially in spring (March to May, which is called yellow dust season), the city can be reached by the yellow dust (HwangSa in Korean), coming from the desert of Mongolia and from China (but in truth there is also a contribution given by local pollution), which forms a characteristic haze and brings breathing problems and eye irritation.
Spring is mild, but the rains increase gradually. The rainiest season, however, is summer, because of the 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 also be periods of good weather, in which it can be very hot, with highs about 35 °C (95 °F).
In Autumn, rainfall decreases, and by October the rains are already quite rare. Here is the average precipitation.
Average precipitation - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDecYear
IncheonJFMAMJJASONDY
Prec. (mm)202040601001103202851555550201235
Prec. (in)0.80.81.62.43.94.312.611.26.12.220.848.6
Days757791015128687102

In August, September and early October (more rarely in July), Incheon can be affected by typhoons, tropical cyclones of South-East Asia, although this area of Korea is less exposed than the southern coast.

Songdo

The amount of sunshine in Incheon is decent in winter, and in spring and autumn as well (although it's lower than in the southern part of the country, like in Busan), and reaches its minimum in July, when cloudy skies prevail (and the sunshine amount goes down to 35%), because of the summer monsoon.

In Incheon, the sea is very cold in winter, but it warms up a lot in summer, reaching 24 °C (75 °F) in August.
Sea temperature - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDec
IncheonJFMAMJJASOND
Sea (°C)5558131722242319149
Sea (°F)414141465563727573665748