How much would it cost to repair an LCD screen of a Nikon camera?

You would have to send the camera to a Nikon service center. They will charge you a non-refundable fee of $100 - $150 to evaluate the problem and give you an estimate. If you elect to have the work done, some of it will be put toward the cost of the labor. Otherwise, you are out the examination fee and you still have a broken screen.

The whole thing depends on the camera. If it is a $1500 DSLR body, that's one thing. If it's a CoolPix, it would probably be easier and as cheap to replace the camera. Consumer-grade cameras are not made to be repaired.