Temple Square is downtown SLC it is definitely worth walking around and checking out the square the temple is beautiful.
The shoreline trail is on the edge of the Wasatch Mountains some of the most beautiful views of the valley and mountain range. It's fairly flat and goes for miles.
Mill Creek Canyon is gorgeous. The main road up the canyon is closed most of the year but it's a nice paved road that is a beautiful walk.
Cottonwood Canyon has some of the best views year round. Lots of hiking and will take you up into the mountains and you can come back through Park City.
Park City is a short 30 minute drive from downtown SLC. They have a great downtown with lots of shopping. Great place to hike, or rent bikes or skis depending on the weather.
Cute little town up in the mountains. Can drive through Provo Canyon down south which is beautiful.
A Swiss town in between Park City and Heber City.
The Salt Flats are about and hour drive straight west of SLC. They are incredibly cool and you can drive directly on the salt which is fun.