This map is a work in progress -- no units are shown and terrain features have not been labeled. I've only recently begun studying this battle in earnest, so I'm hesitant to say too much yet about where individual units were located. In brief, White Plains, New York is at upper right (the streets and buildings of the modern-day city are not visible), and George Washington's army was positioned there, as well as spots further to the north (top) and east (right). The British army (commanded by William Howe) advanced in two columns towards Washington. The left column advanced along the road that runs north from the bottom of the map. The route taken by the right column is not shown (it was further to the east). The left column clashed with an advanced American party near the hill at right-center (I recently wrote about this event). Then the British turned and attacked the American forces on Chatterton's Hill (the big eminence at top-center).
The map is based off a topographic map published in the 1930s. Placement of the roads and woods is based on a handful of 18th and 19th Century maps available in the David Rumsey Historical Map Collection and the Rochambeau Map Collection hosted by the Library of Congress.
Eventually, I'll present an updated version of the map and more information about the battle, but that won't be for quite some time.