or 

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In a similar way, if you are traveling, say, from Rio to Alagoas you can say that you are going up (south-north direction) and down when in the reverse way.

(again, in a way you could state that "você está indo pela BR-101" or "subindo a BR-101 em direção à região norte [nordeste, no caso, mas alguns falam norte mesmo assim.]

To streets, one could think of the next corner or the next traffic lights, according to this discussion.

http://forum.wordreference.com/threads/to-walk-up-down-a-street.899694/

http://forum.wordreference.com/threads/up-the-street-down-the-street.820998/

On this one, the author equals up with "near", and down with "far".

http://forum.wordreference.com/threads/driving-down-the-street.2567140/

On this one "down the street" would mean "along the street".

In a song, I think "indo pela/na rua'' would do.