went down to the canteen

The third one is fine. You could simplify it:

"I went downstairs to the canteen"

It is not often said (but is not wrong), that you "walked" upstairs or downstairs.

You go upstairs, or climb up. Walking is different.

Sorry if that seems picky.

Although the Americans have so-called "walk-up" apartment buildings which means that there is no lift (elevator).

But normally, I would say go upstairs, go downstairs......unless I wanted to make a clear distinction from using the lift (elevator).

Thanks, Mc Tag.