Judging from the sun angle and the orientation of the tracks (basically NW-W to SE-E), I think the picture is looking west towards Summit, NJ, the next stop on the line and the highest point on the Morris and Essex Railroad (builder of this line and purchased by the DL&W prior to this photo). The excellent photo posted by swaool is looking eastward towards Millburn. If it is indeed looking west, it would make the station building on the westbound side of the tracks, which is a bit unusual since most passenger traffic waiting for a train was and is eastbound towards Hoboken/NYC.

I lived in Short Hills for thirteen years, and took the train to points both east and west many, many times from this spot. 111 years later Short Hills is a bit more built up than seen here, but is still a very pleasant community to live, and yes, it does contain many "short" hills.

View from roughly the same angle, 106 years later:

Looks like they're about one hill short.

I have never seen the way the light shades on the poles are placed. It appears that they are upside down but I'm sure they are not. Beside that it looks like it is going to be a nice day as the men hang out watching the woman folk head out on the rear of the train, perhaps a shopping spree in NYC?

between the tracks. I'm pretty sure that this view is the same direction from about where the conductor is standing on the left.

Short Hills was developed in 1879 by Stewart Hartshorne, who made a fortune on window shade rollers. At first, the residents used the nearby Millburn depot, but after the DL&W promised to stop at least two trains here daily, Mr. Hartshorne donated the land and spent $2500 to build this station. He paid the agent's salary here and maintained the building at his own expense for a number of years.

Eventually, this depot was deeded to the Lackawanna, and served the town until 1907, when it was demolished to make room for its replacement. [This information was lifted from "Delaware, Lackawanna and Western Railroad in the Nineteenth Century" by Thomas Townsend Taber]