I'm going to shelter in place down the road in a school. I saw them build it and it has thicker walls of concrete and brick and built better than the wood framed house I'm in now. We went in when they had open house and there's a basement that has emergency food, water and other equipment if needed. The kitchen was fairly well stocked with canned goods, dry goods and a freezer with generator backup. I think it'll depend on who gets there first to claim the stuff. I don't want to get caught out on the open roads if possible. I'm sure people will prey on each other and whittle down the competition at first.
Just remember, a school is a POI known to have medical supplies and shelf stable food, so anyone that passes it will want to visit too, and schools have a lot of windows and entrances.
I always joked that in the event of a zombie apocalypse, Cracker Barrel was the ultimate spot. There's melee weapons on the walls, farming implements to build a garden on the flat roof, a fireplace, blankets, warm clothing, food, shutters that can be repositioned over the windows (or actual, working hurricane shutters in Florida), there are only two easily secured entrances (three for some of the older ones with freezer access from the outside) and they are usually close to truck stops and hotels for convenient scavenging. The problem is that it, too, is a POI on a main path.
It would be a slog, but I plan on going to the family farm on Lookout Mountain and setting up camp over the hill. It isn't an obvious spot, there's spring water, farmable land, the neighbors have cattle, foraging for greens and fruit is good, and there is plenty of lumber to build a palisade for defense.