"Old school" being pretty objective here, since by any standard Neuromancer is pretty quaint by today's standards. I guess I would tend to say anything written before the late '60s, when the influence of SF on popular culture started feeding back into books through other media, and you started to see stuff like Zelazny's Lord of Light and Brunner's Stand On Zanzibar with a new degree of self-awareness that wasn't possible before. (Ringworld, for example, definitely reflected the popularity of Star Trek among SF fans in the late '60s/early '70s.)
I myself was never a big fan of the sacred Asimov/Clarke/Heinlein troika (and I don't know if I ever really thought of Ray Bradbury as "science fiction" at all), but even as a disaffected cynical teenager and post-adolescent in the '80s and '90s, I really liked Theodore Sturgeon (for More Than Human and his short fiction), Cordwainer Smith's "Instrumentality of Man" series, and Alfred Bester's Stars My Destination and Demolished Man. I also read a bunch of Harry Harrison and Richard Matheson (though again, he's probably more of a fantasist). Lately I've been trying to catch up on Jack Vance and Poul Anderson.
There are a number of other older writers I've always meant to get into, but never had the time or wasn't in the mood for, like R.A. Lafferty and A.E. van Vogt. Any suggestions?