I assume that this is a day job or shift work where you can go home at the end of the day as opposed to working on a rig for days at a time. If not there are lots of possibilities to keep a boat anywhere along the Texas/Louisiana/Alabama or even Florida Gulf Coast
But if you are commuting home daily, look at the marinas
in Port Arthur, Orange or even Lake Charles. At the risk of offending locals, this is a pretty scruffy industrial area (except for parts
of Lake Charles) so don't expect first class accomodations.
In so far as hightailing it to Galveston, I recall
a friend who kept his boat in Galveston Bay as a hurricane
was bearing down on the area. He ran it down to Port Aransas to get out of the storm's path. Guess where the hurricane hit?
So buy good insurance
and be prepared to evacuate yourself inland if a storm threatens, but don't move the boat.