Oh man, now we're talking my language! Where are you coming from? I know you said any type of cuisine would do, but SLC is a decent sized city and has a TON of places to eat. We don't really have a local fare that is unique to Utah, but we have some great places to eat. Some of what you've been told are fantastic options. Here would be my picks for certain types of food.
Mexican food: Red Iguana
Burgers: Lucky 13 (and I really like Rich's Burgers on Broadway and From Scratch is pretty good too)
Philly cheese or meatball sub: Moochies
BBQ: Pat's BBQ (R&R is pretty good as well, but I'm partial to Pat's)
Pizza: The Pie or Litza's (I'm a sucker for Litza's...)
Greek: Padeli's Street Greek
High end Steakhouse: Flemmings or Ruth's Chris (RC is everywhere, though)
Expensive buffet with incredible views: The Roof (people have a love-hate with this place...you either love it, even though it's expensive, or it's way overpriced. Not really a middle ground)
You seriously have almost a never ending option of food places, just depends on what you are in the mood for and where you will be at the time.