The main problem that you are going to find is that there is VERY little public hunting land in Texas. I believe that 95% of land in the state is privately owned. That also leads to the "State land" being over-hunted.
Also, unless you are in an open county, squirrel hunting season is closed until May 1.
Both Harris and Galveston counties are not open counties so they are not available for hunting (Harris doesn't have much land where it is legal to hunt anyways).
The counties with no closed season for Squirrel are as follows: Brazos, Burleson, Collin, Dallas, Ellis, Falls, Grayson, Grimes, Kaufman, Madison, Milam, Rockwall.
Remember, you must
have a hunting license to hunt squirrel in Texas, even if you are in a county with no closed season.
This page will help you with county regulations:
You will also have to purchase an Annual Public Hunting Permit for $48 in order to hunt on any public land in Texas.
And this map will show you counties around Houston that *might* have squirrels to hunt.
Personally, I think that it is a lot of trouble to go through just to hunt squirrels...