'Up' is going to be relative to the speaker, so where are you standing?
If you're standing at the bottom of the map (in the street), then the tree is at the 'mouth', 'entry', 'front' or even 'front end' of the alley. There are probably more options as well.
If you're standing towards the top of the map, then the tree is 'down', 'at the end', the 'back', the 'exit' or maybe even 'the head' of the alley.
Note too that with most trees, 'drooping' signifies something's wrong with the tree, especially something like a maple tree. Willows might be the exception, because they naturally droop.