Depends on what you are doing. If we are talking King's Peak, the most common trailhead is Henry's Fork, but to get to that you have to go up into Wyoming and back down into Utah, about a 3.5 hr drive if I remember correctly. There are additional trailheads that will take you there on the south of the Uintah range but they add more mileage and I'd have to look them up. Those trailheads are probably 2.5 hr away from Salt Lake City.
Another way to get to King's Peak is via the Highline trail starting from Mirror Lake (2 hr away fro m SLC). The bad news is that King's Peak is about 40 miles away! I only mention this because the Highline trail is one of the most scenic, desolate and scary thru hikes in the country (about 70 miles each direction), nearly 80% above the tree line, almost entirely above 10,000 ft, makes 8 summits and typically only accessible during the height of the monsoon season in the Uintas so lightning storms abound! One of the nice things about the Highline is that you can hike 2 days out and 2 days back and get in as much mileage as you want and plenty of scenery. There are so many lakes to dip your Tenkara rod in as well along the way!
If you are looking for more of a loop than an out-and-back there are plenty of those as well. Again, I'd have to look them up. Let me know if you'd like me to do some research for you.