Crash
I see you have a C4. How familiar are you the known "problem areas" on the earlier cars? If you are not well versed, you would be well advised to take someone knowledgable with you to help you look the car over.
The C3 had basically the same frame as the C2 cars had. The frame is always an area of concern on these cars and since I see you are in upstate NY and assuming that's also where the car is salt has a tendency to take it's toll over the years on car frames. Look the frame over very carefully for rust and any places rotting thru. The kick-up area right in front of the rear wheels especially is a problem area. Surface rust is fine and can be easily cleaned up, but anything beyond that is cause for concern as frame repairs can get real expensive real fast.
When I go to check out a car I usually bring a sharp, pointy tool like an awl, icepick, or screwdriver with me to poke the frame in lots of places. If it feels soft you have concerns you need to look at - it it goes thru when you are poking it than you have MAJOR problems to deal with.
Also check around the entire birdcage area. Birdcage rusting is a major issue and very difficult and very expensive to repair. Most of the birdcage is not visible or accessable so you need to look for telltale signs such as rust or bubbling of the paint because of rust underneath it along the birdcage areas such as the door jambs and along the windshield area.
Fresh, new paint is always nice but to me that makes me look at a car even harder as I start wondering why someone is selling a car they just spent money to paint. is the new paint there to hide other problems??
Check thru operation of everything running off the vacumn system such as the headlights and wipers.
Check fit on all panels, especially the doors, hood alignment, and where the rubber front and rear pieces join the body.
check for evidence of leaks around windshield, doors, rear window, and t-tops. Check condition of weatherstripping. Weatherstripping can be replaced without TOO much trouble but it's a bit of a PIA and it's not cheap to buy all new weatherstripping.
these are just a few areas to look at