I'm working at the post office on the west side of this town.
Which countries are considered Western countries?
If you eat makizushi on Feb 3rd of this year, you have to face west.
The West side of something is known as the West or the West side. Sorry, I have no story to go along with your West side.
The readings are the kun'yomi vocab readings. You should know both of them, with 西 being にし and 側 being がわ (what you learned with the kanji).