We usually use north, south, east, west, not northern, southern, eastern and western, to refer to specific places or to direction of movement. We can use north, south, east and west as adjectives or adverbs and occasionally as nouns:
More and more people are buying second homes on the south coast of Ireland. (adjective)
After Bangkok, we drove north for about six hours without stopping. (adverb)
Strong Atlantic winds are forecast in the west of Portugal. (noun)
We normally use capital letters in place names with north, south, east and west:
The conference is taking place in North Dakota.
[from an advertisement in a travel magazine]
Bargain flights to South America from London Gatwick from £350.
Northern, southern, eastern and western: larger areas
We commonly use northern, southern, eastern and western (without capital letters) to refer to larger areas or territory. We can only use them as adjectives:
The northern parts of India have suffered severe flooding.
Houses are more expensive in most western parts of the country.
Some names of specific places have capital letters for northern, southern, eastern and western:
We are holidaying in Northern Ireland next year. (name of a region)
Perth is the capital of Western Australia. (name of a state)
San Diego is my favourite place in southern California. (a part or region of a state but not the name of a state)