I'm really fond of story-rich RPGs set in modern-era (i.e. late 20th century) Earth, but when I try to think of classic examples, only Earthbound comes to mind.
What else fits this description?
There are quite a few set in a modern-era, on the Super Famicom at least.
The SMT series is modern.
Idea no Hi and Maka Maka
Adventures of Hourai High
In fact, a lot of the Megaten games are, or at least partially.
It's not stuck in the 50s, it's set in the style of future predicted by the 50s.
2161 ain't the good old days, it's what happens when you have a world that didn't invent transistors and then picked a fight with China.
OP asked for late 20th century, not mid-22nd.
I'm curious as to what specifically you're referring to, but hesitant to ask since this isn't /v/.
I also was mistaken about the Fallout universe's lack of transistor; it was invented, but about a hundred years later than had occurred in our timeline. It came only a handful of years before the world blew up, so I guess it didn't really make a difference.
Bethesda's take on the series setting, I'm not so sure it's deserving of criticism. The gameplay certainly, but I think they did a fairly good job of bringing the same design and aesthetics into their take, at least for the first Fallout game they did. I have nothing good to say about New Vegas, so if that's what you meant, I agree entirely.