Carotid artery
From Memory Alpha, the free Star Trek reference.
The carotid arteries are responsible for delivering blood containing oxygen and nutrients to the brain in most humanoid species. There is one carotid artery on each side of the typical humanoid neck. This artery is often used as the injection point for hyposprays containing intra-arterial medication. The size of these arteries, and their proximity to both the surface of the skin (at the neck) and to the brain make them an excellent choice for most such medications.
When Khan Noonien Singh was revived from suspended animation, he held a knife to Leonard McCoy's throat and demanded to know where he was. McCoy refused to answer, but offered a suggestion to Khan, that it would be most effective to slice the carotid just under his ear. (TOS: "Space Seed")
When Harry Kim, serving on the USS Voyager, was attacked by a member of Species 8472, the Doctor injected nanoprobes through his carotid artery. (VOY: "Scorpion, Part II")
