I generally agree. Union County is more suburban. The urban section being that around Elizabeth/Linden/ Hillside etc.
The portions of Union around Mountainside, New Providence, Berkely Heights etc. are definately upscale suburban. I classed it as I did because it really didn't fit in with the heavily urban criteria for the county as a whole.
I used to live in one of those upscale areas you mentioned. The Watchungs are a pretty area.
For what it's worth, Union County is counted as being in the NYC Metropolitan Area by whoever looks after such things, as are Middlesex, Monmouth, Ocean, Somerset, Morris, Sussex, and Hunterdon Counties from your list. Including Hunterdon in the NYC Metropolitan Area might be a stretch -- it has some rural areas as I remember.