I can't tell you anything about check in because I have never cruised from Charleston. Having been there many times I can tell you traffic should not be a problem. Taxi would be the way to go because it is quicker and there would not be much difference in the cost. I would estimate about $30 with a travel time of about 30 min. If nothing unusual happens you should be ok.
54 Carnival: Mardi Gras, Ecstasy X2, Fascination X6, Celebration, Elation X5, Glory X5, Fantasy X4, Valor, Holiday X3, Imagination, Liberty, Spirit X2, Freedom, Destiny X2, Splendor X2, Dream X2, Conquest, Legend X3, Victory, Sensation, Paradise, Inspiration, Magic X2, Triumph, Miracle, Breeze, Sunshine X2
6 Norwegian: Sky, Jewel, Dawn, Epic, Pearl, Breakaway
7 Windjammer: S/V Legacy X3, S/V Polynesia, S/V Caledonia, S/V Diamant, S/V Sagitta