Okay, LOTS of options to suggest:
1. You're driving up from Tempe eh? That means you'll go past some good sites in Arizona (Red Rock territory around Sedona, Page--where Antelope Creek Canyon and maybe the world's most famous slot canyon is located).
2. Southern Utah on your way to SLC...tons of slot canyons (around Escalante), Zion, Bryce, San Raphael Swell, the Arches, Capital Reef National Park (winter is a great time to go there)....they're spectacular in winter or especially if there's snow.
3. Let's talk Salt Lake City (which was what you originally asked about):
--I love Antelope Island (it's in the middle of the Great Salt Lake)...some great rocks, cool causeway, free range Bison, some great rock formations. Hint: if you want the high ground and cool rocks with a great view, you want the NW section of the island (can't remember the name).
--The Municipal Library in SLC is lovely, very modern architecture.
--There is an arboretum there up near the University of Utah that is lovely. Not sure what it's like in snow or cold weather but might still be worth a try.
--Little Cottonwood Canyon next to the city is great.
--You've got Temple Square if you're in to all that (LDS temple and buildings, etc.)
--Liberty park is big (about 80 acres) and has a nice aviary if you want to shoot birds. The SLC zoo isn't bad either...I remember shooting a very playful polar bear there.
--The old train station is cool (now a series of restaurants and museum if I remember but great on the outside).
--If you go north of the City, there is Hill AFB with a bunch of planes you can climb all over or get in the cockpits of.
--The Bonneville Salt Flats are great to shoot but it will be a drive outside of SLC.
--You're very close to Park City and that is lovely (especially when it's snow season). In fact, any of the ski resorts near by are good shooting...from stuff in the lodge to skiers, to the beauty of new snow on mountain peaks, sunrise/set, et.
--Don't forget, the winter Olympics were held here so there are a bunch of Olympic facilities you can shoot.