You can enter three buildings on Second Street (overgrown, scorched, and the subway tunnel on the far left), the plot progresses when you've reached the end of all of them. If you haven't found Second Street yet, try exploring every building on First Street.
(If you're stuck in the access tunnel that leads from the truck/outskirts to First Street, there's a key on the table with a lot of junk which lets you open the locked door)