Salt Lake County really doesn't have a courthouse anymore. This used to be the old one, which is city hall:
http://virginiayung.files.wordpress.com/2011/11/romanesque.jpg
Instead, cities have their own justice courthouses. This is Salt Lake City's ... which I'm not a fan of:
http://img.deseretnews.com/images/article/midres/1350076/1350076.jpg