Ensign Peak Trail is a very popular trail among the locals. It starts just outside of downtown Salt Lake City. Ensign Peak is fantastic for families of all sizes. When you get to the top the view of the mountains are amazing. Round trip it is only 1 mile, and has an elevation gain of 398 feet. At the beginning and end of the trail is plaques that tell its historical significance, which makes it a fun history lesson. It also has spiritual significance for members of the Church of Jesus Christ of Latter Day Saints. To get there go to the State Capitol, then keep driving up the mountain into the neighborhood until you cannot go any further. You will see an LDS church right next to the trail head.
The trail is open till 10:00 PM, and it is fun to see the Salt Lake valley on a summer night, but don’t stay too long. You will get a parking ticket after 10:00pm. The downside to this trail is even on a clear day you still have the Salt Lake City smog, and there is a lot of dog feces and other garbage littering the trail. Feel free to bring a bag and help clean up some of the litter. There is a trash can at the beginning of the trail.
Utah State Capitol
Another fun item while you are there is to go to the State Capitol. The granite building is remarkable. There is a trail path surrounding the Capitol that is lined with benches and trees. There are other interesting statues around the Capitol building, for example: Mormon Battalion statue, Native American, beehive, and even some Lion statues. You can also schedule a tour at utah.gov.