Some of the best of Heinlein’s “Future History” stories take place in the 20th. century. As do many other of his short stories.
Everything that takes place in Spider Robinson’s “Callahan’s” series does, but it’s best to start with the earlier collections. Some of those tales were so “present day” that Analog subscribers wrote in to complain about the lack of science fiction…
Clifford Simak’s “Way Station”, is a nice rural tale when it starts. As is “Special Deliverance”, in it’s own way.
There are a few related books by Tim Powers that cover 1940-2000, but those may be more fantasy than you are looking for.
Another vote for the Cyberpunk genre. Gibson’s latest book takes place RIGHT NOW, it seems. And Neal Stephenson’s alter-ego Stephen Bury has written a few thrillers that take place in modern day…
Yeah, check out “Interface”, I think you’ll like it, if this bit:
…is what you’re looking for.