Tree stands are your friend when you're just starting out. Barns can be handy (usually a shotgun or crossbow in there) but also tend to have a lot of zombies around them. Fire stations, same thing - lots of zombies but tend to have nice gear in them (found an AR one time and a large pack). Most of the military spec guns are going to be clear up in the airbase, which is crawling with zombies and usually bandits will camp here to kill people that wander in.
Super markets are also a good place for supplies, some of them can be find on the edge of small towns making them a LOT easier to sneak into without attracting zombies.