There's no pulp mags published anymore (or crappy ones, no real original ones that QT must have read). But you can sure look for them in secondhand book stores like Black Mask (they started a book company later on, so you can find the same authors writing short stories in the mag and publishing novels for the company), Dime Detective, Ellery Queen's Mystery Magazine, Amazing Stories.
For comics, you have Doc Savage and Weird Tales, that you can now still found and which are the best. Doc Savage (war stories) comics are still easy to find in old book stores and Weird Tales (horror stories) published collected comics in book (not mags).
Concerning authors, you might know them already cause they mostly become famous when they started to publish novels and not short stories anymore. Such as Philip K. Dick, Elmore Leonard, Conan Doyle, Chandler, Jim Thomson, Robert Bloch, Lovecraft, Cornell Woolrich, HG Wells, Bradbury, William S. Burroughs, David Goodis, upton Sinclair, and so on. So basically now that you have a list, you can look for their short stories and even if you don't read them in pulp mags, those are the same published in pulp and now collected in books.
I hope it helped you, feel free to ask anything else if you want