Hi!
NBO is the closest big airport to the game areas. The closest is Kilimanjaro.
From NBO or Kili you can drive to the Mara. You can also fly from both, and fly from Dar-es-Salaam.
Kenya Airways, BA, KLM, Virgin, Air France, Swiss, Emirates, and a bunch of others all fly to NBO (so does Lufthansa cargo, Atlas, MK, Southern, etc). Probably DAL/NWA/KLM/AF will work best for NBO
cliff
NBO