The Butler Fork Trailhead services many different hikes into the southern end of the Mount Olympus Wilderness. You can access Dog Lake, or the peaks of Circle All, Gobbler's Knob and Mount Raymond. The saddle that leads up to those three peaks allows for a few flat places to throw up a tent and do an overnighter in the Wasatch. The steep trail is definitely a little tough with a full pack, but it's less than 2 miles and is mostly in the shade, making for a quick and mostly unexposed hike. The wildflower laden trail has amazing views in just about every direction once you reach the saddle. From Circle All Peak you also get views of Kessler Peak and Storm Mountain, and just about every major peak of Big Cottonwood Canyon is visible from this general area, up and down canyon.
The steep grade of the entire hike minimizes the options to pitch a tent before you reach the saddle, and even once up top the flat spots are limited, so you may have to camp closer to the trail than you'd prefer. However, the the morning views overlooking Mill A Basin here are fantastic. Mount Raymond has a healthy and thick aspen forest at its base that goes crazy in autumn. One great thing about doing an overnighter here is the opportunity to tackle its peak while cutting out the first 1.7 miles and 1,500 feet of gain, making it much easier to complete. Moose, deer, hummingbirds and marmots are all common here, and so are fellow hikers, but you rarely will see other backpackers. It wouldn't make for a great place to camp in the woods for multiple nights because of the lack of room to spread out or find privacy. It does, however, make for a fun place to spend the night in the mountains and catch an amazing sunset and sunrise without a lot of hassle. Plus, the trailhead is only 15 minutes from the suburbs of east Salt Lake.