Here is a list of places you want to avoid when Shit Hits The Fan, it will also depend on what type of SHTF situation it is. (Not in any specific order)
Government buildings - The government will not be helping you when it all goes to hell, your odds of getting shot by the government are way higher.
Military Bases - This one is a no-brainer, they will not help you and you may get shot.
Police Stations - Yes they have guns there, but there is probably gonna be police there as well, and if there is not police there, well other people probably will be.
Hospitals/Doctors Offices - Both hospitals and doctor offices will be over whelmed, they wont be able to help you because they will have hundreds of people waiting for help already and most of them won't get it, so learn how to take care of the ill in your family.
Airports - When SHTF all flights will be canceled, so the odds of you getting on a plane are extremely small (Unless you own a plane at a private airport)
Big Cities - If you're in a big city and you're trying to leave, good luck, you and only a couple thousand of other people will have the same idea, if you're smart, you'd leave sooner or if it is too late to leave, just wait 3 to 4 weeks till most of the people have either moved on or have been killed.
Grocery Store(s) - This is the #1 place people will hit first because they need food & water and guess what? They're going to get hurt and possibly get killed too.
Places where hundreds/thousands of people gather