Very good thought and research has been put into this question. Most of the reason the question even arises has to do with visual perception.
We will keep going down the road until we find it.
This sentence will be universally understood by English speakers to mean: We will continue to travel on this road until we find it..
In English, "go down the road" will mean "travel on the road" because of old perceptions,.
With few extreme exceptions, if one tries to follow a road visually into infinity, one perceives the road falling in the far distance, not rising. That, because of the curvature of the earth. So, in English, it is "down the road", no matter any measurable incline or decline. I would not think most English speakers think height when hearing or saying "down" in this sense.
As to the specific question:
This street leads to the facility that you're looking for.
"down" is not needed. "Street leads" supplies sufficient information. It would not be incorrect to use:"street leads down", but only because of the fixed idiomatic use of "down" in matters of travel. Travel, in this case, can mean more than moving from point to point on the earth's surface.
Sometime down the road will will need new regulations on this practice.
Down the road can mean into the future.Macmillan Dictionary on line