Oh Mai is a definite for me every time I go to SLC. Awesome Thai joint. Their garlic butter ribeye steak banh mi is the best I've ever had. Their brisket pho is awesome as well!
For Mexican food, Red Iguana and/or El Asadero are my two favorites. Both have excellent, authentic dishes and you'll leave full. There are some really good Mexican food trucks in SLC also if you don't need the restaurant scene.
If you like sushi and/or Japanese food, Takashi is really good, and so is Naked Fish and they're both downtown.
For more traditional favorites, I usually will go to Ruth's Diner. And if I'm hungry for Italian, or an awesome deli sandwhich, I'll go to either Tony Caputo's or Moochie's.
That's all I've got. Hope it helps.