According to Steven Miller (not the Space Cowboy) it's not in the morning when you wake up! And the answer involves science: chronopharmacology -the study of the interaction of biological rhythms and drug action- to be exact.
Without getting too science-y, the best time to drink coffee (or a caffeinated beverage) is between 9:30 and 11:30am (based on waking up around 8:00am). Why? Here's where the science comes in: cortisol! Our bodies naturally produce this hormone throughout the day, and levels peak between 8 and 9:00am, right when most of us are waking up or starting our days. Cortisol follows our body's circadian rhythm, which most of you should know relates to sleep/wake cycles. It makes sense that our bodies would be most awake in the morning, and it's no surprise that cortisol promotes alertness.
Basically, drinking coffee during peak levels isn't helping, since it's effect on alertness is not needed (hence the jitters some people experience). It makes too much sense to have that coffee later in the morning, after your natural alertness has subsided a bit. Who couldn't use an extra boost before lunch?
More, including what a "zeitgeber" is, at Co.Design