I painted mine pretty much all Walmart primer grey.
The area inside the "garage" where the shuttle is serviced I painted white. Also the smaller section of scaffolding to the left of the "garage" (when you are looking at the front), the pole that connects the "garage" section to the launch tower, and the big lightning rod on top of the launch tower I also painted white.
I looked at tons of photos. The only parts that consistently looked white were the "garage" and the lightning rod. The other white parts were either repainted or it was a trick of the light that made them look grey.
Also the walls in the center of the launch tower were definitely either red or grey. I suspect the red must have been the color when it was first built as newer photos show it the same grey as the rest of the tower. I built this model when it first came out and I reburbished it several months ago. I originally painted this section red.
I left that section red and painted those other parts white just for the exact reason you mentioned about not having an all grey boring looking complex.