TexasCHLforum.com

Texas is a pre-emption state, which means local municipalities may not make laws which pre-empt state laws on the carrying of concealed weapons. Since state law states that CHL holders cannot be barred from government owned or leased facilities, the city ordinance has no effect:

Local Government Code § 229.001. Firearms; Explosives
(a) A municipality may not adopt regulations relating to the transfer, private ownership, keeping,
transportation, licensing, or registration of firearms, ammunition, or firearm supplies.
(b) Subsection (a) does not affect the authority a municipality has under another law to:
(1) require residents or public employees to be armed for personal or national defense, law enforcement, or
another lawful purpose;
(2) regulate the discharge of firearms within the limits of the municipality;
(3) regulate the use of property, the location of a business, or uses at a business under the municipality's fire
code, zoning ordinance, or land-use regulations as long as the code, ordinance, or regulations are not used to
circumvent the intent of Subsection (a) or Subdivision (5) of this subsection;
(4) regulate the use of firearms in the case of an insurrection, riot, or natural disaster if the municipality finds
the regulations necessary to protect public health and safety;
(5) regulate the storage or transportation of explosives to protect public health and safety, except that 25
pounds or less of black powder for each private
(6) regulate the carrying of a firearm by a person other than a person licensed to carry a concealed handgun
under Subchapter H, Chapter 411, Government Code, at a:
(A) public park;
(B) public meeting of a municipality, county, or other governmental body;
(C) political rally, parade, or official political meeting; or
(D) nonfirearms-related school, college, or professional athletic event.
(c) The exception provided by Subsection (b)(6) does not apply if the firearm is in or is carried to or from an
area designated for use in a lawful hunting,

This tells me that municipalities can regulate the carrying of firearms by persons not licensed by the State, but cannot regulate the carrying of firearms by people with a CHL.

Of course, I am not a lawyer, nor did I stay in a Holiday Inn Express last night.