The legal definition is in section 1.07 of the Penal Code. It says:
(40) "Public place" means any place to which the public or a substantial group of the public has access and includes, but is not limited to, streets, highways, and the common areas of schools, hospitals, apartment houses, office buildings, transport facilities, and shops.
Note that it does not mention ownership at all. Clearly, the common area of a shop is still private property (owned by some person or corporation). The legal question is then what is meant by access. Note than an unfenced front lawn is accessible to anyone (ok, let's say no posted signs on trespass). Can a delivery person walk up there? That is an easy way to think of access by the public.
But that is just the physical access. Courts have ruled that access does not have to be physical, but might be simply visual access. Can the public look in and see it? Then it is a public place. The way I was taught relied on the Fourth Amendment and may be a little harder for some to understand, but here goes. An exception to a search warrant exists if it is in plain view. This is defined as being where it can be seen by a police officer who is in some spot where he can legally be and he does not need to take any physical action to see it (such as lifting a cover or turning something around). If the cop could claim plain view on some evidence he saw, then that is a public place. So, a front yard is a public place, as is a back yard that doesn't have a privacy fence. Even your living room could be a public place if there is a large window and the curtains are open. There is actually a court case on that one from someone who liked to stand at a window while undressed.
And, to return this to the original topic, note that the disorderly conduct law makes it illegal to display a firearm in a public place in a manner that is calculated to alarm. You might not want to pose your classic Gatling gun in the living room with the barrels pointed out the uncurtained window. And if you can't do that, you certainly cannot carry your weapon openly on common area streets in your subdivision.