It varies state to state. In some states you need to have a license to carry at all, some require a permit for concealed carry, some allow for businesses to ban firearms(some states it is just a polite request sign with no legal force), some ban carry in parks(national parks or otherwise.).
Nationwide there are certain locations where guns are prohibited like courthouses, government buildings, post offices, political events, etc.
So in most states you can have a permit to carry and have no problems carrying concealed anywhere except the federally prohibited locations. In some states you can carry concealed but must disarm before you go into a business or location with a certain sign. A few states, even with a permit, you can’t use public transit or take a shortcut through a park or go to most businesses if you are in the wrong part of the state. In a couple states you can’t carry a firearm except one that is unloaded and in a case directly between your house and the place that you are lawfully allowed to use it. You can have a magazine that holds more rounds than a certain number of round or a type of firearm legally under state law and then unknowingly enter a city or county that you are not allowed to have that and potentially face legal consequences without the intent to break a law just because a road passes through the boarder of that jurisdiction.
You really have to consider the USA to be 50 different countries, more like the EU, than having consistent laws. You can be totally fine having a loaded AR-15 on you back and cross a legal line and commit a serious crime once you walk a foot into a different jurisdiction.