In no particular order here are the storytimes in Spanish (or bilingual English/Spanish) I found for Salt Lake County:
Chapman Branch: Every Thursday @ 7 pm
Day-Riverside Branch: Every Saturday @ 11 am
Main Library · 1st & 3rd Mon. of the month, 7 p.m.
Sprague Branch · 4th Wed. of the month, 11:00 a.m.
Kearns Library - Family bilingual storytime on the last Monday of every month @ 7 pm
Please let me know if you know of any other storytimes in Spanish that aren't listed here or if you've been to any of these storytimes.