Common carotid artery is palpable at:
Common carotid: It is a branch of brachiocephalic trunk on right side and a direct branch of arch of aorta on the left side. The artery runs upwards along medial border of stemocleidomastoid muscle enclosed within the carotid sheath. The artery ends by dividing into internal carotid and external carotid at the upper border of thyroid cartilage.
The anterior tubercle of the transverse  process of the sixth cervical vertebra is the largest of all suchprocesses and is called the carotid tubercle of Chassaignac. The common carotid artery can be best pressed against this tubercle, deep to the anterior border of the sternocleidomastoid muscle.
Key Concept:
Upper border of thyroid cartilage lies at C3-4 vertebral level. Common carotid artery bifurcates into two branches at this level.
Reference: B D Chaurasia’s Head and Neck anatomy, 6th ed page no 79
Upper border of thyroid cartilage
Upper border of cricoid cartilage
At hyoid bone
Lower border of cricoid cartilage