Most visitors are very safe in the United States, but still need to pay attention to the thief at the crowded places. Locations frequented by tourists and visitors (National Mall in Washington DC, and Manhattan in NYC) often have a police presence and are quite safe. Non-white travelers in some white-dominant rural areas and small towns might encounter stares. These are mostly out of curiosity and should not result in hostile actions.
American health care is good, but the most expensive in the world. As a traveler you should have travel insurance or you will potentially face very high costs if you need medical care. During any emergency, dialing 911 on any telephone will connect you to a dispatcher for the emergency services in the area (police, fire, ambulance, etc). Calls to 911 are free from pay phones and any mobile phone capable of connecting to any local carrier.
American police officers are always armed while on duty. If stopped by the police, you should stay calm, be polite and cooperative, avoid making sudden movements, and state what you are doing if you need to reach for your purse or wallet to present your identification. Do not do anything unless told to do so. If you follow the officer's instructions, you will probably not be arrested.
In addition, the weather and natural disasters also need attention. Hurricanes in June through November in the South including Florida, blizzards in New England and the areas near the Great Lakes and the Rocky Mountains, tornadoes mostly in the Great Plains region, earthquakes in California and Alaska, floods in areas of the Midwestern United States and wildfires in the late summer and early fall in Texas and on the West Coast, particularly California. You'd better check the weather or other informations before travel.
Recreational drugs are prohibited by federal and state law. In some states, such as California and Alaska, holds a small amount of marijuana is considered bad behavior, but there may have been a fine and / or imprisonment. Holds over one ounce of illegal drugs, including cocaine, ecstasy, LSD, heroin, hashish is a felony punishable by long prison terms. Foreigners, any drug-related conviction will be grounds for expulsion.
Firearm is legal in all jurisdictions with varying degrees of restriction by State, Territory, and Federal District. The vast majority of Americans are non-violent except in self defense. Non-immigrant aliens that are in the country for fewer than 180 days cannot possess a firearm or ammunition, unless they came here specifically for hunting or sporting purposes, or they have a valid hunting license from the state they are visiting.