What significance does the vacant lot, the church, and the hospital have in The Outsiders?What happens at these locations, and why are they important to the story?
I don't think any of these locations have any special symbolic significance in The Outsiders. The vacant lot was chosen as the site of the rumble because it was a safe place for both the greasers and Socs.
"Nobody in this neighborhood's going to call the fuzz," Steve said grimly. "They know what'd happen if they did."
The abandoned church on Jay Mountain outside Windrixville serves as the hideout for Johnny and Ponyboy. It seems like a perfect, pastoral setting for the two boys, who needed to lay low and clear their heads for a few days. Dally had previously scouted the area as a hideout for himself, so he knew it would be a safe haven for the boys. When the church burns (because of the boys' lit cigarettes), it also becomes the site of the three boys' heroism when they enter the burning building to save the trapped children inside.
The hospital is where Pony and Dally recover from their burns, and it is where they visit Johnny several times before he dies.