Best Fish to Catch in Morehead City Billfish. Most out-of-state anglers coming here will be doing it for the Billfish bite, so we may as well kick things off with these superstars. ... Tuna. ... Mahi Mahi. ... King Mackerel (Kingfish) ... Redfish. ... And More! ... Charter Fishing. ... Shore Fishing. Aug 15, 2024