You realize that you'd probably be better off going down to Port O or Port A? I would think the fishing would be better (less pressure), and the drop off of the continental shelf is significantly closer (50-60 miles as opposed to 100-120 miles). So even though you might save a little more traveling in the car, it would probably be lost gas in the distance you've got to travel offshore.
Or even Freeport. This above is my reason for questioning Galveston as a choice.
Having lived in Houston for 20 years (1976 - 1996) and still a frequent visitor I can't even imagine towing a boat down I 45 from Conroe to Galveston unless you did it at 3 or 4 AM. For me that would be the mother of all white knuckle drives.
Driving to Freeport, Port O'Connor, Matagorda or Port A would somewhat further but you don't have to travel as far in your boat for the fish and I would bet that fishing would be much better.