By author:
Karin Slaughter (American coroner & detective team, set in the south; series)
Walter Mosley (American PI, set in South Central LA in the 60s; series)
Mo Hayden (not a series but writes good mysteries)
Michael Connolly (American detective series, set in current LA, LAPD offshoot)
Robert Crais (American detective series, set in current LA, some connections to LAPD)
Greg Iles (not a series, but good one off mysteries)
Dan Fesperman (American author, Bosnian detective, 2 in the series; also has other thrillers that are good)
Ian Rankin (Rebus, the Scottish detective we all know & love; series)
Ruth Rendell (Inspector Wexford mysteries, series)
Robert Wilson (British author, Spanish detective series)
Stella Remington (Former MI5, two novels so far)
Arturo Perez Reverte (Spanish mystery novels, not a series but very good)
Peter Tremayne (Sister Fidelma, Irish nun and her Anglo Saxo co-hort solve mysteries in early Ireland; series)
Ellis Peters (Cadfeal, the Welsh monk who solves mysteries in his spare time; series)
That should keep you busy for a while, all the books should also be easily available at your local library.
Love mysteries!!
Those should keep you busy for awhile.