I studied Judo in Utah county (Lindon, UT), but since you asked specifically for the Salt Lake area, here is what I could find in your area. It's a fairly large club. There are probably more "hidden" clubs in the SLC area.
SALT LAKE JUDO CLUB
HEAD INSTRUCTOR: DANIEL FUJIKAWA
CLUB ADDRESS: SALT LAKE DISTRICT PARK
PHONE: 808-834-6157
PRACTICE TIMES: MONDAY/WEDNESDAY/FRIDAYS - 6:00 - 8:30
SATURDAYS - 10:00 - 11:30 AM
FOR MORE INFORMATION CONTACT: DANIEL FUJIKAWA
PHONE: 808-834-6157
CLUB HISTORY
SALT LAKE JUDO CLUB WAS STARTED IN JANUARY 1985 BY DANIEL FUJIKAWA WITH FAMILY MEMBERS WILLIAM, SAM, DERRICK, AND DEAN ALONG WITH LOYAL FOLLOWERS AND STUDENTS JOHN KELIIHOLOKAI, ROSS TANAKA, AND RON IWAMOTO. THE CLUB BEGAN WITH 8 INSTRUCTORS AND 5 STUDENTS. SINCE IT STARTED THE CLUB HAS TRAINED NUMEROUS STUDENTS THAT HAVE BECOME RESPECTED CITIZENS IN THE COMMUNITY IN ADDITION TO NATIONAL AND INTERNATIONAL LEVEL COMPETITORS.