The city and county building at Washington Square is an interesting example of late 1800s looking architecture, Which may be inspirational to steam punks or architecture geeks. A few bronze statues and a fountain are on the west lawn. There are also several annual festivals which use the lawn and street as a venue, including Salt Lake Pride, Living Traditions, Salt lake City Arts festival and a couple others. The rest of the year however, most people will find very little at this site.
Washington square is a popular hangout for the less fortunate which may be off-putting to some. However it is worth a look if you're planning on visiting the City Library. I suggest taking the city library's elevator to the top floor and seeing the CC building from the roof.