I can't speak for the best place out of the Houston area, but I can give you a little perspective on what's happening a little to the east of you.
Out of the Beaumont area, most spearfishing trips originate out of Sabine Pass.
Out of our area, the slope of the Gulf equates to something along the lines of about 1.5 to 1.75 feet per mile. So, in order to hit decent depth's you generally have to be about 40 or so miles offshore.
I know of a group that went out this weekend, but ended up returning early due to mechanical problems on the boat.
They reported poor vis with a high amount of murk (6-10' max) and water temps in the mid 60's at about 35 miles out. I havent been out to the rigs myself yet this year, but generally conditions in the area less than 35 miles out aren't even worth bothering with and some days, even 60 miles isnt far enough to make it worth it.
Moving further down the coast towards Freeport, etc. the depth drops off much more rapidly, and I've heard reports of good vis at nominal depths as close as 20-30 miles out.
If your plans include spearfishing rather than just sightseeing and you have never done this at a rig before, let me know and I will offer you some tips.
Regardless, watch out for discharges or workers who are present that might accidently be dropping things. May also be a good idea when inquiring with boat captains to find out how many trips they have done this year, what conditions have been like, how far they have had to go out, etc.