It's a bit of a cheat, but Bozeman Yellowstone International Airport (BZN) is approximately 150 km from the geographic center of Yellowstone National Park. Of course, Yellowstone National Park is huge; the closest point in the park is "only" about 75 km away as the crow flies, while the farthest point is about 200 km away. The park headquarters are 96 km from BZN.
Similarly, as pointed out by @user71659, Fresno Yosemite International Airport (FAT) is approximately 105 km as the crow flies from Yosemite Village. This is perhaps a bit less of a cheat than the Yellowstone case, since while there is not a town called "Yellowstone" in Yellowstone National Park, there is a town called "Yosemite Village" in Yosemite. (This does stretch the definition of a "city", of course.)