Final answer:
King Agrippa was the one who visited Caesarea and to whom Festus asked for advice regarding Paul's case as described in the New Testament.
Step-by-step explanation:
The king who came to Caesarea to visit when Festus asked him for advice about Paul's case was King Agrippa. In the context of the New Testament, particularly in the Acts of the Apostles, there is an account of Paul being held as a prisoner and presenting his case before Festus. Festus, being uncertain about how to proceed with Paul's legal situation, sought the advice of King Agrippa who was visiting Caesarea at that time. This event is significant as it showcases the early interactions between Christian figures such as Paul and the ruling authorities of the time.