Keep and eye out for 30.06 and 30.07 signs. 30.06 prohibits concealed carry, while 30.07 prohibits open carry.
If you open carry, it must be in a belt or shoulder holster. Obviously you were going to use a holster anyway, but I mention it just because it's on the books.

This includes while in a vehicle, it needs to be holstered if unconcealed.
Don't carry at institutions of higher education.
Don't carry where there is a TABC 51% sign, which is going to be places like bars, where their revenue comes largely from alcohol sales. The sign should be red like this:
https://www.tabc.state.tx.us/publications/brochures/weapons51.pdf
Here is the "blue" sign, which is probably about what you saw at Walmart:
https://www.tabc.state.tx.us/publications/brochures/weapons.pdf
You will see something like this in places that sell alcohol for off-premises consumption or at restaurants that serve alcohol, but not enough to be forced to have the red 51% sign. When legally carrying you can still carry at these places.
Don't carry to where a high school, collegiate, or professional sporting event or interscholastic event is taking place.
Trying to summarize here, can't guarantee my accuracy... Hopefully I haven't forgotten something obvious.
Oh and welcome to Texas

Hope you enjoy your stay