In SLC:
- The main Salt Lake Library downtown is one of the coolest libraries in the country and has great views of the valley from the roof of the building.
- Right next door to the library is the Leonardo museum. Which in itself is cool, but they are also doing a mummy exhibit right now which is worth seeing.
http://www.theleonardo.org/
- City Creek Center (shopping, restaurants).
http://www.shopcitycreekcenter.com/
- Utah Museum of Natural History
http://nhmu.utah.edu/
-Temple Square
- Multiple parks, trails all over the place
Food: Depends what you want. Plenty of good restaurants, pubs, clubs, etc. downtown.
FYI, when you are downtown, you can use the light rail and bus system for free unlimited rides in the "free fare zone" which is an easier way to get around some of the attractions and you won't have to find parking.
http://www.rideuta.com
Go to:
http://www.visitsaltlake.com/ for more ideas.
Within 30-45 mins driving:
- Park City. Plenty to do there.
- Utah Olympic Park. Near Park City.
http://utaholympiclegacy.com/
- Snowbird. Good scenery, food. Take the tram ride to the top.