up the street/road, etc.
A2
along or further along the street/road, etc.
Dictionary examples:
The pizza delivery guy ran up the street, chased by hungry dogs. (0.0)
The robot mailman rolled up the street, delivering letters to confused dogs. (0.0)
The clown rode his tiny bicycle up the road, honking loudly. (0.0)
They live just up the street. (11.8)