This turned out to be hard to find, but not impossible...
The Teach US History web page you linked to contained an interesting footnote:
(4) Marks, Arthur S. “The Statue of King George III in New York and the Iconology of Regicide,” The American Art Journal 13 (Summer 1981): 62
That article stated that the statue was a duplicate of one installed in London and also contained this further interesting footnote:
As to the appearance of Wilton's statue, we are stymied. As will be seen, neither monument -- that erected in London or in New York -- exists any longer; nor is there any visual record known of either. No topographical drawing or print, or sculptor's drawing, for example, has come to light which might give a specific sense of what the statue had looked like.9
- However, for the New York version there are some early plans of the area which locate the Bowling Green and the position of the statue's pedestal in its midst; see Stokes, vol. 1, pls. 46Aa, 46Ac, pp. 356-57, 360.
Stokes is The Iconography of Manhattan Island, 1498-1909, which does contain this description and this drawing of the area as it existed then:
Plate 46 A-a
A Plan of Fort George at the City of New-York
Wash drawing on paper. 17 x 27½ Date depicted: c. 1773
Author: Claude Joseph Sauthier.
Owner: Library of Congress, Div. of Maps and Charts (Faden Collection, No. 95).
This plan is the most complete and detailed representation of the Fort that we possess. It must have been drawn prior to December 29, 1773, when the buildings in the Fort were destroyed by fire, and after August 16, 1770, as it shows the statue of George III, erected on that day in the Bowling Green. This statue was demolished on July 10, 1776, although the pedestal remained until 1818 (see Pis. 51 and 52).
To save you a trip through a badly constructed PDF, Plate 46Aa looks like this:
Plate 46Ac turned out not to be interesting for this question.
The fence is exactly the same fence today as then, and is in the same location, so the statue would have been approximately where the George Delacorte memorial plaque currently is, at the northern edge of the fountain.
As you can see, America has largely forgotten that a statue of King George III ever stood here, and indeed, this park is also known as Evacuation Day Park to commemorate the departure of the last British troops on November 25, 1783.