On a 1992:
1) Coil spring seats. GM powder coated most of the suspension parts in 1992, and over time, even in areas without much salt use, the powder coat breaks down, trapping moisture against the metal. Which eventually causes its failure. The coil spring seats are notorious for collecting water, holding water against the metal, and suffering failure. Can be a pretty serious issue, and the only way to fully and properly inspect is disassembly of the entire strut tower assembly off the car. On-car inspection is not possible.
2) Lower cooling hose/pipe assembly. Directly exposed to road grime/etc., and the metal part beneath the coolant recovery reservoir tends to rust out.
3) Leaf Spring seats -- the rubber "ends" of the fiberglass leaf spring often 'dissappear' over time, leaving the fiberglass leaf spring end to directly rub. Makes a bunch of noise when you hit bumps. But still worthy of inspection and of course, repair when necessary.
4) Rear brakes, especially the e-brake. Tend to seize up and become inoperable.
5) Stock front-brakes suck. If you're doing the inspection and/or addressing the coil seat problem as described in #1, do yourself a favour, hit a junkyard, and get a set of new steering knuckles/strut tower assemblies off of like a 1997 Lumina or something. Make sure to grab the brake rotors as well.
Other than that, welcome to the forum! I have a 1992 Oldsmobile Cutlass Supreme, and that's basically a synopsis of what I've gone through.