As posted above, you get a natural spike within the first few hours of falling asleep. GH is normally only released from the pituitary when the blood sugar levels are low. If after the GH release blood sugar levels rise enough to trigger insulin, the liver uses the insulin and the GH to synthesize IGF-1 and release it in the bloodstream.
So the question then becomes what do you take your GH for.
If you want pure fatloss, then early-morning a few hours before eating, will work best, as well as sometime around your workout. If you want to take GH for muscle gain, follow injections with meals. If you are taking GH for rejuvenation, any of these will work.