Cascade springs. One of the most amazing springs I know. It is a good sized stream originating straight out of the side of the mountain with a series of small cascades and pools. Plan time for photo ops and you'll gain an appreciation for our mountains.
You can enter from I-15 into American Fork canyon passing Timpanogos Cave (well worth seeing on it's own) then on to Cascade Springs. You can keep going south past Sundance Ski Resort (also worth visiting) and down to Provo canyon and can make a quick stop at Bridal Veil Falls and on down to Orem/Provo.

In SLC you can go to Lucky13 next to Smith's Ballpark for drinks and great burgers.

Other attractions worth seeing:
-City Creek Mall
-Hogle zoo & drive up Emigration canyon
-This is The Place Heritage Park/ Monument
-Brighton Ski resort/Big Cottonwood Canyon/ SilverLake boardwalk
-LaCalle Restaurant $$$
-Homestead Crater hot springs (advance purchase)
Heber Creeper Railroad ride
-Park City
-Antelope Island (bison)
-Simpson Springs pony express/ mustang watching
-SLC temple Square closed for renovation but you can walk the gardens on top of the Conference Center

Thats just a few off the top of my head. If you want more information boardmail me.