There are activities no matter the season or skill level. In spring, there are waterfalls everywhere. In autumn, spectacular colors of foliage. Winter is ski season and summer is great for hiking or just a nice drive. But to really experience the Wasatch, you must get out of your car. The rewards will be well worth it.
If you're not into hiking, take the Tram at Snowbird Ski Resort and get whisked to the top of an 11,000 foot peak for million dollar views. In summer, Snowbird also has an alpine slide, mountain coaster, and music festivals. Alta is next door and Albion Basin has thousands of wildflowers blooming in the summer.
Brighton and Solitude ski resorts are up Big Cottonwood. But there are nice easy hikes from Donut Falls and Silver Lake to more advanced hikes like Broads Fork Twin Peaks or Dromedary Peak and countless in between. Plenty of areas for a good afternoon bbq too. You could also take Guardsman Pass to Park City or Heber. This is especially nice in the fall time.
The Cottonwood Canyons (Big and Small)
They are not far town (30-40 minutes maximum to the entrance), yet they provide a great escape from the city’s problems, winter inversions, summer heat. In the winter time this is the location of many of the finest skiing resorts, Alta, Solitude. However when it is snowing you will need a 4 x 4 to get to these locations up the canyon. During the summer heat the canyons provide lower temperatures and beautiful scenic hikes and camping. A wonderful side trip if you have a day to spend in nature.
Sat here by the freezing water of Big Cottonwood Canyon for more than an hour. Most relaxing moments of my Salt Lake summer.