The US Navy has come up with a process that manages to take Hydrogen and Carbon Dioxide out of seawater and convert them into long chain hydrocarbons, such as jet fuel or gasoline. The process uses electrical energy to drive the reaction, and obviously requires more energy than they get out of it in fuel. But if the electricity is generated from reactors or some other carbon neutral method, then this will be one method to get fuel. Their production ship can produce fuel at about $6 / gallon, but since about half of that cost is for the ship itself, a shoreline based system should cost about $3 / gallon.
Hopefully the process doesn’t involve releasing the CO2 from the seawater into the atmosphere. Since the process needs the carbon atoms, I expect they use almost all of the carbon they get from CO2.