Oh, the the Box of Pine Creek is so pretty. It works best as a car shuttle, though, so you'd probably want to set that up unless you plan to just reverse the trail on your way out. It's 9 miles one way, top to bottom (which is the route I'd recommend, but it can be done the other way too of course) from the Upper Box and Lower Box trailheads. It's really nice because it goes from mountain forest to desert canyon, and you have the water all the way. There can be poison oak in the canyon, so keep an eye out for that. Should not be terribly crowded. I think dogs are supposed to be leashed when in the canyon, check with the Escalante Ranger District to be sure.
Some other possibilities in the general area might be The Gulch down the Burr Trail, the Moody canyons, and exploring out around Willow Gulch, Forty Mile, and Broken Bow Arch, which are waaay down HITRR, so the likelihood of seeing a ton of people there is low. I haven't done the Moodys yet but there are threads on here about them.
