Here is a link to the Utah Chess Association webpage. This site has a wealth of information. They list upcoming local tournaments as well as locations and meeting times for chess clubs around Utah. There is also information about local instructors as well as scholastic chess in Utah. If you are interested in playing chess in person over the board in Utah, this is a great place to start.
Local Events

Kind of short notice but there is a tournament this Saturday (3/17/12) at the University of Utah. It is the Utah G/60 Championship. Go to www.utahchess.com. It is right on the front page.

There are lots of local tournaments in Utah. The best place to go for information is www.utahchess.com.
The Utah Open starts tomorrow, October 25. The Utah Closed and the Utah Amateur are in November, December features a Beginner Brawl as well as a tournament for non-beginners. There is a tournament every Saturday (except Saturdays on which a bigger tournament is scheduled) afternoon in the library at SLCC (4700 South Redwood Rd). Most of the tournaments include at least 2 sections to help faciliate matching up players of even strength. There are also a variety of scholastic tournaments.
I'm on the board for the Utah Chess Assocation and as always happy to answer questions about live chess in Utah.

There is sometimes some stuff in St. George, but not in Cedar City (to my knowledge).
The live OTB stuff now is just the weekly quicks at SLCC on Saturday afternoon. Size limited and only adults at the moment.

http://www.utahchess.com/event/6th-annual-salt-lake-open/?instance_id=1914
There is one this Saturday in Draper
If you know about a live tournament in Utah, post an advertisement here.