Well, again, it sounds like you need to narrow down what sort of SF/spec fic sub-genre you want to work in. It defines your world; the mystery is just what you run through it. Asking whether there are SF writers out there other than Asimov implies you really need to connect with SF before you can consider writing anything in that genre.
Start with some Robert Heinlein, Phillip K. Dick, Kurt Vonnegut, Ray Bradbury, Ursula LeGuin, Frank Herbert, Orson Scott Card, Arthur C. Clarke and of course George Orwell. This will give you the classics across multiple sub-genres. Then look at the last 10-15 years of Hugo Award nominees (
http://www.thehugoawards.org/). This will show you what's happening now.
If you're of a more literary bent, Margaret Atwood (
The Handmaid's Tale), Cormac McCarthy (
The Road) and Michael Chabon (
The Yiddish Policeman's Union) are good examples of how "serious" authors tackle speculative fiction. (Chabon's is also a good example of a mystery set in an alternative-history universe).
BTW: I don't know what you consider vulgar, but if you haven't read William Gibson's
Neuromancer or
Burning Chrome, or Neal Stephenson's
Snow Crash, you've missed the foundations of cyberpunk.
Once you're done with this, then you can start looking at how mysteries can co-exist with a fantastical world. Some possibilities:
Walter Mosely,
Futureland. Noirish excursions into a dystopian future by Easy Rawlins' creator.
J.D. Robb's
...in Death series. Romantic suspense;
Naked in Death is the first. A female NYPD detective in 2058 hunts down murderers and her brooding antihero flame.
Len Deighton's
SS-GB and Robert Harris'
Fatherland. Complimentary detective stories set in similar alternative-history worlds, both hinging on a German victory in WWII.
Asimov's
The Caves of Steel. You may have read this if Asimov is your fave; a human detective hunts murderers with a robot partner.
Eric Garcia,
Anonymous Rex. Tongue-in-cheek sendup of
noir detectives in a world in which dinosaurs didn't die out. Yes, there is a mystery here.
Some other lists:
IO9:
http://io9.com/5526900/top-10-greatest-science-fiction-detective-novels-of-all-timeAkron-Summit County Public Library list of SF/F detective series:
http://www.ascpl.lib.oh.us/internetresources/pop/favfiction/sfdetective.pdfA similar but not overlapping list from Wikipedia:
http://en.wikipedia.org/wiki/List_of_fictional_science_fiction_and_fantasy_detectivesNPR's list of Top 100 SF/F books:
http://www.npr.org/2011/08/11/139085843/your-picks-top-100-science-fiction-fantasy-booksGood luck!