First game board to use hexagonal tiles?
One possible answer could be the game Agon (sometimes called "Queen's Guards" or "Royal Guards"). I ran across a reference to the game in the book "A world of chess: its development and variations through centuries and civilizations" (Cazaux, J., &amp; Knowlton, R., 2017). They state the following:


  Perhaps the earliest recorded board game using hexagonal cells is Agon, a very original strategic Pawn game first published in 1842.


There were some claims that the game originated in the 18th century, but apparently the first published record of the game can be verified as 1842.

Cazaux, J., &amp; Knowlton, R. (2017). A world of chess: its development and variations through centuries and civilizations. Jefferson, NC: McFarland &amp; Company, Inc., .