I was lucky enough to get street parking but your best bet is probably City Creek parking. Still, my street parking was almost 2 blocks away & it was a very cold walk to the theater.
Around the corner .. Southwest corner
If you get there early enough you can also sometimes snag street parking! Just depends on what you want to spend - all the other suggestions are great. I work occasionally at the theater and use Regent Street parking when needed.
Regent street parking as well. They do $5 event parking and it is right near the theatre.
I parked in the underground parking for City Creek. First 2 hours are free, first 3 if you get a restaurant validation then $2/hour after.
Over behind pierpont avenue oyster bar. 10 for the night.
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