In Texas, while traveling in a vehicle, the firearm must be concealed. It can be loaded (or not, to preference).
The signage has to meet certain requirements (and will be easy to spot if compliant).
30.05 No unlicensed carry (a very rare sign to see)
30.06 No concealed carry (even with LTC/CHL)
30.07 No Open carry (even with LTC)
No carry in amusement parks (so like SeaWorld in S.A.; Six Flags in Arlington, or the waterparks), race tracks (auto or horse), large sporting arenas, no government buildings, typically.
No magazine limits, or ammunition type limits. Do watch the County limits signs for "Burn Ban In Effect" signs, as that can restrict things like campfires and the like.
Can't speak to the other States, other than NM and CO are going to be tougher to travel through for having more restrictions.
Should this be in the "Legal" forum?
The Texas concealment requirement for carrying in a car now does not apply if you are 21 or older or have an LTC. Previously, before Constitutional Carry, you could conceal carry in a car even without an LTC (but it had to be concealed).
The Texas Penal Code changed last year with Constitutional/Permitless Carry.
Look at 46.02 (a-1)
(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle ... in which:
(1) the handgun is in plain view,
unless the person is 21 years of age or older or is licensed to carry a handgun under Subchapter
H, Chapter
411, Government Code, and the handgun is carried in a holster;
https://statutes.capitol.texas.gov/Docs/PE/htm/PE.46.htm
Sec. 46.02. UNLAWFUL CARRYING WEAPONS.
(a) A person commits an offense if the person:
(1) intentionally, knowingly, or recklessly carries on or about his or her person a handgun;
(2) at the time of the offense:
(A) is younger than 21 years of age; or
(B) has been convicted of an offense under Section
22.01(a)(1),
22.05,
22.07, or
42.01(a)(7) or (8) committed in the five-year period preceding the date the instant offense was committed; and
(3) is not:
(A) on the person's own premises or premises under the person's control; or
(B) inside of or directly en route to a motor vehicle or watercraft that is owned by the person or under the person's control.
(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle or watercraft that is owned by the person or under the person's control at any time in which:
(1) the handgun is in plain view, unless the person is 21 years of age or older or is licensed to carry a handgun under Subchapter
H, Chapter
411, Government Code, and the handgun is carried in a holster; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic or boating; or
(B) prohibited by law from possessing a firearm.