Island Hopper,
You can do some shore diving in Offatt's Bauou (off 61st in Galveston) You can park you car and make entry right there. Weekdays are beat. Lots of boats, etc. on weekends. The viz can go from 3-4 feet to 10-15 feet, depending. It is current free. A number of the commercial dive schools do their training there. Depth is 0 to about 30'. Can be pretty silty/muddy on bottom. Lots of big rocks around the edge. Can find stone crabs (suggest use of tongs) English Bayou is also divable.....it is just across the street from Offatt's. They are connected by water running under a bridge on 61st St. The Galveston Bay complex is OUT for rec diving, too muddy. You can dive the Galveston jetties, BUT....it's all about timing. Clear water has to be in, you have to watch the tide changes carefully, and you'll need a boat. All that said, diving the jetties can be pretty interesting. I've seen viz at 30-40 feet over the years (highly unusual) 3'-8' would be good. Also week days are best. I've seen some pretty big fish out there.
Lots of people go to Twin Lakes, I do sometimes because I live 5 minutes from there, it's easy diving and I have yet to meet my first A-- Ho-- out there. I know, give it time and anything is possible. A great bunch of divers frequent the place. Hope to see you around.
Regards,