What to say about that amazing park, amazing mountains, shapes, rocks...
My suggestion: Go there in winter! The contrast of the red-sand and red-rocks with the snow is superb!
All the information: maps, fees... in the following web-site:
The Timpanogos National Park is a mere 1/2 hour outside of Salt Lake City. This national park I had no idea existed before arriving, I sure as anything want everyone to know about it since.
In the park you've got several choices. You can take a hike towards the peak. Go camping. Or climb to the Timpanogos Caves.
The Caves are the highlight and there is a charge to take the cave tour. During summer its an idea to arrive early and book straight away as only limited numbers can enter the cave. The climb to the cave is quite challenging due to it being 1hr uphill at high altitude, but the rewards are spectacular.