It's pronounced Wilkes-Barre. (Wilkes-Berry.) Named After John Wilkes, an English radical and journalist and Isaac Barre, an Irish soldier and son of a French refugee.
It's the first thing they tell you when you get hired at a local radio or television station. It's not Wilkes-Bear or Wilkes-Berra...WILKES-BARRE. And by the way, it's always hyphenated. (That means there's a dash between Wilkes and Barre for those of you in Glen Lyon.)
You may ask how I can be so certain about this? I was told by a man from Beemington, NY during a meeting in Ceilingsgrove.