front trunk, rear trunk, and everything inbetween
seriously
The " hell hole " is the biggest thing to check. It is the area in the engine bay below the battery. They almost always rot out there, and once that is opened up the water/acid mix runs into the passengers longitudinal and start rotting from the inside out. I have seen quite a few cars that LOOKED fine from the outside of the long and suspension console, until the paint was stripped away.
The first thing to walk away from is if the passengers door gap is tight, particularly if the door drags or won't open at all. This is a sure sign the chassis is folding up from rust. Check the cowl in front of the windshield where the rubber strips are. That gets to be an involved repair. Check the rear trunk pan, check the front trunk pan, pull the seats forward and remove the carpet from behind them and check the floor there from the top side AND the bottom side. If the floor tar is still intact on the inside you won't see jack shnit. Check the back firewall between the pass compartment and engine compartment. The sound deadening pads held water and rotted out that wall. Check for folds or ripples in the sheet metal around the wheel wells and forward of them.
So yeah, check the front trunk, the rear trunk and everything in between