The paper Christenfeld, Choices from identical options, Psychological Science, 1995 (pdf) made observations as follows:
A public restroom at a California state beach was used for this study. The men's room had four identically sized stalls, and each stall had four identical toilet paper dispensers. The stalls were side by side, with Stall A closest to the door. The toilet paper dispensers were lined up in a horizontal row on the occupant's right.
They enumerated the results as follows:
Here's a color-coded version:
So they observed a preference for the middle bathroom stalls (along with the middle toilet paper dispensers).
More generally, this phenomenon appears to be also known as the center stage effect, and is used in marketing psychology.