Ahhh I don't have a deep sea fishing recommendation but if you're up for other types of fishing, go KAYAK fishing, it is really a blast! Go with "J&L Kayaks" - when we went it was a whole lot of fun and they are really nice people. Totally worth it.
According to the users review, you can go to the North Myrtle Beach Fishing Charters. It offers full services and deep fishing adventures across the beach. See http://nmyrtlebeachfishingcharters.com/ for reference.