up, down
‘towards/away from the centre’
Up and down are not only used to refer to higher and lower positions. They can also refer to more or less important or central places. (Trains to London used to be called ‘up trains’, and trains from London ‘down trains’.)
- The ambassador walked slowly up the room towards the Queen’s throne.
- She ran down the passage, out of the front door and down the garden.
- We’ll be going down to the country for the weekend.
But in the US downtown refers to the central business/entertainment area.
North and south
People often use up and down for movements towards the north and south (perhaps because north is at the top of a map page).
- I work in London, but I have to travel up to Glasgow every few weeks.
‘along’
Sometimes both up and down are used to mean ‘along’, ‘further on’, with little or no difference of meaning.
- The nearest bank is about half a mile up/down the road.