I thought this was a fun question, so I did some digging. I went into Diio Mi (an airline industry tool, but most people here probably already know that) and pulled the unique destinations for all of the airports that I could think of that could vie for this title. I looked at unique nonstops flown during the past year (1 June 2017 through 31 May 2018) and found the following:
Overall:
FRA - 324
CDG - 317
IST - 283
AMS - 272
MUC - 271
PEK - 250
ATL - 246
ORD - 245
LGW - 239
DXB - 230
DFW - 226
PVG - 222
BCN - 221
MAD - 217
CPH - 214